Additional Mathematics 0606: INTERSECTION POINTS Topical Past Paper Questions

Solutions to this question by accurate drawing will not be accepted. A circle $ C_{1} $ has centre (3, 5). The point $ P(1,4) $ lies on circle $ C_{1} $. A circle $ C_{2} $ has centre (12, 8). The line with equation $y = 19 - 3x$ is the common chord of circles $C_{1}$ and $C_{2}$…

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 equat…

(a) The curves $4x^2 - 3y^2 + xy = 24$ and $y = \frac{2}{x}$ intersect at the points $P$ and $Q$. Find the coordinates of $P$ and $Q$. [5] (b) Find the length of $PQ$. Give your answer in the form $a\sqrt{b}$, where $a$ is rational and $b$ is the smallest possible integer. [2]