Mathematics Pure Math 1 9709: INTERSECTION POINTS Topical Past Paper Questions

In the diagram, AB is a chord of the circle with equation $ (x-6)^2 + (y-3)^2 = 20 $. The two tangents to the circle with equations $ y = 2x + 1 $ and $ y = -2x + 25 $ meet the circle at the points A and B respectively. (a) Find the coordinates of the points $A$ and $B$. b) Hence…

Find the set of values of the constant k for which the quadratic equation $ 3kx^{2}+(k+8)x+3=0 $ has two distinct real roots.

The equation of a curve is $ y=\frac{1}{2}k^{2}x^{2}-2kx+2 $ and the equation of a line is $ y=kx+p $, where k and p are constants with $ 0<k<1 $. (a) It is given that one of the points of intersection of the curve and the line has coordinates $ \left(\frac{5}{2}, \frac{1}{2}\rig…