Additional Mathematics 4037: Coordinate geometry of the circle Topical Past Paper Questions

A circle has equation $ x^{2}+y^{2}-25=0 $. A second circle has the same radius as the first circle, and the coordinates of its centre are both positive. The two circles intersect at the points A and B. The line AB has length 6 and is parallel to the line y = -x. Find the equatio…

## DO NOT USE A CALCULATOR IN THIS QUESTION (a) Find the exact distance between the two points where the curve $ 9(x-1)^{2}+4(y-3)^{2}=36 $ cuts the y-axis. (b) Find the coordinates of the points where the curve with equation $ 2x^{2} + 83xy = x^{3}y - 20x $ intersects the curve…

The line with equation $ x+3y=k $, where k is a positive constant, is a tangent to the curve with equation $ x^{2}+y^{2}+2y-9=0 $. Find the value of k and hence find the coordinates of the point where the line touches the curve. [9]