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# 11 x1 t11 01 locus (2012)

## by Nigel Simmons, Teacher at Baulkham Hills High School on Jul 26, 2012

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## 11 x1 t11 01 locus (2012)Webinar Transcript

• Locus
• Locus LocusThe collection of all points whose location is determined by somestated law.
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y x
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y 4 x
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y 4 4 x
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y 4–4 4 x
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y 4–4 4 x –4
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y 4–4 4 x –4
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y 4–4 4 x –4
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y P  x, y  4–4 4 x –4
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y P  x, y  4  x  02   y  02  4–4 4 x –4
• Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin y P  x, y  4  x  02   y  02  4–4 4 x x 2  y 2  16 –4
• (ii) A point moves so that it is always 5 units away from the y axis
• (ii) A point moves so that it is always 5 units away from the y axis y x
• (ii) A point moves so that it is always 5 units away from the y axis y P  x, y  x
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y  x
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y x
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 1 –1 x
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 P  x, y  1 –1 x
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 P  x, y  1 –1 x
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 x  y 1 P  x, y  3 12   1 2 1 –1 x
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 x  y 1 P  x, y  3 12   1 2 1 x  y 1  3 2 –1 x
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 x  y 1 P  x, y  3 12   1 2 1 x  y 1  3 2 –1 x x  y 1  3 2
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 x  y 1 P  x, y  3 12   1 2 1 x  y 1  3 2 –1 x x  y 1  3 2 or   x  y  1  3 2
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 x  y 1 P  x, y  3 12   1 2 1 x  y 1  3 2 –1 x x  y 1  3 2 or   x  y  1  3 2 x  y 1 3 2  0
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 x  y 1 P  x, y  3 12   1 2 1 x  y 1  3 2 –1 x x  y 1  3 2 or   x  y  1  3 2 x  y 1 3 2  0 x  y 1  3 2
• (ii) A point moves so that it is always 5 units away from the y axis y  0, y  5 P x, y   x  0   y  y   5 2 2 x x 2  25 x  5(iii) A point moves so that it is always 3 units away from the line y = x + 1 y y  x 1 x  y 1 P  x, y  3 12   1 2 1 x  y 1  3 2 –1 x x  y 1  3 2 or   x  y  1  3 2 x  y 1 3 2  0 x  y 1  3 2 x  y 1 3 2  0
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. y x
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y x
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y  x,0  x
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y  0, y   x,0  x
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y  5d  x,0  x
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d  x,0  x
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x(v) A point moves so that its distance from (1,2) is the same as its distance from (5,–4).
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x(v) A point moves so that its distance from (1,2) is the same as its distance from (5,–4). y x
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x(v) A point moves so that its distance from (1,2) is the same as its distance from (5,–4). y 1, 2  x  5, 4 
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x(v) A point moves so that its distance from (1,2) is the same as its distance from (5,–4). y 1, 2  P  x, y  x  5, 4 
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x(v) A point moves so that its distance from (1,2) is the same as its distance from (5,–4). y 1, 2  P  x, y  x  5, 4 
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x(v) A point moves so that its distance from (1,2) is the same as its distance from (5,–4). y Perpendicular bisector of (1,2) and (5,–4) 1, 2  P  x, y  x  5, 4 
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x(v) A point moves so that its distance from (1,2) is the same as its distance from (5,–4). y Perpendicular bisector of (1,2) and (5,–4) 4  2 1, 2  mAB  5 1 P  x, y  6 x  4  5, 4  3  2
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x(v) A point moves so that its distance from (1,2) is the same as its distance from (5,–4). y Perpendicular bisector of (1,2) and (5,–4) 4  2 1, 2  mAB  5 1 P  x, y  6 x  4  5, 4  3  2 2  required slope  3
• (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. P  x, y  y d  0, y   x  x    y  0  5  x  0   y  y  2 2 2 2 5d y 2  25 x 2  x,0  x y  5 x(v) A point moves so that its distance from (1,2) is the same as its distance from (5,–4). y Perpendicular bisector of (1,2) and (5,–4) 4  2 1, 2  mAB   1  5 4  2  M AB   5 1 ,   2 2  P  x, y  6 x    3, 1 4  5, 4  3  2 2  required slope  3
• 2y  1   x  3 3
• 2 y  1   x  3 33y  3  2x  62x  3y  9  0
• 2 y  1   x  3 33y  3  2x  62x  3y  9  0 OR
• 2 y  1   x  3 3 3y  3  2x  6 2x  3y  9  0 OR x  1   y  2    x  5   y  4  2 2 2 2
• 2 y  1   x  3 3 3y  3  2x  6 2x  3y  9  0 OR  x  1   y  2    x  5   y  4  2 2 2 2x 2  2 x  1  y 2  4 y  4  x 2  10 x  25  y 2  8 y  16
• 2 y  1   x  3 3 3y  3  2x  6 2x  3y  9  0 OR  x  1   y  2    x  5   y  4  2 2 2 2x 2  2 x  1  y 2  4 y  4  x 2  10 x  25  y 2  8 y  16 8 x  12 y  36  0
• 2 y  1   x  3 3 3y  3  2x  6 2x  3y  9  0 OR  x  1   y  2    x  5   y  4  2 2 2 2x 2  2 x  1  y 2  4 y  4  x 2  10 x  25  y 2  8 y  16 8 x  12 y  36  0 2x  3 y  9  0
• 2 y  1   x  3 3 3y  3  2x  6 2x  3y  9  0 OR  x  1   y  2    x  5   y  4  2 2 2 2x 2  2 x  1  y 2  4 y  4  x 2  10 x  25  y 2  8 y  16 8 x  12 y  36  0 2x  3 y  9  0 Exercise 9A; 1aceg, 3a, 4, 6, 8, 10, 11, 13, 14