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QUESTIONS1- Sketch the circle x2 + y2 = 4.Find the center and radius first. -The equation is in the form x2 + y2 = r2, so we have a circle, center (0, 0) with radius r = √4 = 2
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2- Sketch the circle (x − 2)2 + (y − 3)2 = 16Find the center and radius first. -The equation is in the form (x − h)2 + (y − k)2 = r2, so we have a circle with centre at (2, 3) and the radius is r = √16 = 4.
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3- Sketch the circle (x + 4)2 + (y − 5)2 = 36 -We have a circle with centre at (-4, 5) and the radius is r = √36 = 6.
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4. Find the equation of the circle withcentre (3/2, -2) and radius 5/2. -Centre (3/2, -2) radius 5/2
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5- Find the points of intersection of the circle x2 + y2 − x − 3y = 0 with the line y = x − 1. -We solve the 2 equations simultaneously by substituting the expression y = x -1 into the expression We have:
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So we see that the solutions for x are x = 1 or x = 2. This gives thecorresponding y-vales of y = 0 and y = 1.So the points of intersection are at: (1, 0) and (2, 1).We can see that our answer is correct in a sketch of the situation:
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