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### L1 Circle.pptx

• 1.
• 2.
• 3. Conic Sections (Conics) •Formed by intersecting a double-napped cone with a plane •Circle •Parabola •Ellipse •Hyperbola
• 5. Circle •a conic section that is formed by intersecting a cone with a plane that is perpendicular to the axis of the cone •the set of all points in a plane that are equidistant from a fixed point called the center
• 6. Standard Form of the Equation of a Circle (x−h)2 + (y−k)2 = r2 where (h, k) is the center of the circle r is the radius, r > 0
• 7. Example 1. Determine the standard equation of the circle given the coordinates of its center and the length of its radius a. center at (2, -3) and r= 3 (x−h)2 + (y−k)2 = r2 (x−2)2 + [y−(−3)]2 = 32 (x−2)2 + (y+3)2 = 9
• 8. Example 2. Given the standard form of the equation below, find the coordinates of the center and the radius. a. (x+9)2 + (y−1)2 = 25 Center is at (-9, 1) and r=5 (x+9)2 + (y−1)2 = 25 [x− (−9)]2 + (y−1)2 = 52
• 9. General Form of the Equation of a Circle x2 + y2 + Dx + Ey + F = 0 Ex. x2+ y2 + 3x + 12y + 2 = 0 x2 + 2y2 -4x + 2y + 1 = 0
• 10. Transforming the Equation of a Circle from the General Form to the Standard Form and Vice Versa
• 11. Example 3. Determine the standard form of the equation of the circle defined by 4x𝟐 + 4y𝟐 - 4x + 24y + 1 = 0 1 4 (4x2 + 4y2 - 4x + 24y + 1 = 0) 4 4 x 2 + 4 4 y2 - 4 4 x + 24 4 y + 1 4 = 0 x2 + y2 - x + 6y + 1 4 = 0 (x2 - x )+ (y2 + 6y)= - 1 4 (x2 - x + 1 4 )+ (y2 + 6y + 9)= - 1 4 + 1 4 + 9 (x − 1 2 ) 2 + (y + 3)2 = 9
• 12. Example 4. Determine the general form of the equation of the circle defined by (x + 5)2 + (y−6)2 = 4 (x + 5)2 + (y−6)2 = 4 (𝑥2 + 10x + 25) + (𝑦2 - 12y + 36) = 4 𝑥2 + 𝑦2 + 10x - 12y + 25 + 36 – 4 = 0 𝑥2+ 𝑦2+10x- 12y + 57= 0
• 13. Graph of a Circle •The rectangular coordinate system (Cartesian Coordinate Plane) is used to sketch the graph of a circle. The graph provides a clear view of its center and radius
• 14. Example 5. Write the equation for the graph of the given circle below Center is at (0,0), r= 2 (x−h)2 + (y−k)2 = r2 (x−0)2 + (y−0)2 = 22 𝑥2 + y2 =4 x y 0 1 2 -2 -1 -2 -1 1 2
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