A-Level CAIE Mathematics AS 1.3 Coordinate geometry Question Bank

Find the coordinates of the point at which the perpendicular bisector of the line joining (2,7) to (10,3) meets the x-axis.

A line has equation y=3 x-2 k and a curve has equation $y=x^{2}-k x+2$, where k is a constant. Show that the line and the curve meet for all values of k.

Find the set of values of m for which the line with equation y=m x+1 and the curve with equation $y=3 x^{2}+2 x+4$ intersect at two distinct points.

Find the set of values of m for which the line with equation y=m x-3 and the curve with equation $y=2 x^{2}+5$ do not meet.

Find the set of values of k for which the curve $y=k x^{2}-3 x$ and the line y=x-k do not meet.

A line has equation y=2 x-7 and a curve has equation $y=x^{2}-4 x+c$, where c is a constant. Find the set of possible values of c for which the line does not intersect the curve.

Points A and B have coordinates (5,2) and (10,-1) respectively.

The point M is the mid-point of the line joining the points (3,7) and (-1,1). Find the equation of the line through M which is parallel to the line $\frac{x}{3}+\frac{y}{2}=1$.

Two points A and B have coordinates (1,3) and (9,-1) respectively. The perpendicular bisector of A B intersects the y-axis at the point C. Find the coordinates of C.

The equation of a curve is $y=x^{2}-6 x+k$, where k is a constant.