Coordinate Geometry of the Circle (Cambridge (CIE) O Level Additional Maths): Exam Questions

Solutions to this question by accurate drawing will not be accepted. A circle has equation $x^2+y^2–16x–10y+73=0$.

(i) Find the coordinates of the centre of the circle and the length of the radius.

(ii) Hence show that the point (10, 6.5) lies inside the circle.

A different circle has equation ${(x–10)}^2+{(y–6.5)}^2=2.25$. Show that the two circles touch. You are not required to find the coordinates of the common point.

A circle has a centre $(2,–4)$ and radius $3$.
The line$y=2x–3$ intersects the circle at points $A$ and $B$.
The perpendicular bisector of line $AB$ intersects the circle at points $X$ and $Y$.
Find the area of kite $AXBY$.