Coordinate Geometry of the Circle Structured Questions | Cambridge O Level Additional Mathematics

Question 1 of 4 · 11 marks

Coordinate Geometry of the Circle · 3 - Tangent-to-Circle Problems

4 parts

Additional Mathematics 4037 · Question 1Paper 2 · Calculator[11 marks]

The point $A(6, 4)$ lies on the circle $C$ with equation $(x-2)^2 + (y-1)^2 = 25$ .

(a)

Find the equation of the tangent $T$ to circle $C$ at point $A$ . Give your answer in the form $ax + by + c = 0$ , where $a, b, c$ are integers.

[3]

(b)

Tangent $T$ intersects the $x$ -axis at point $P$ and the $y$ -axis at point $Q$ . Calculate the area of triangle $OPQ$ , where $O$ is the origin.

[3]

(c)

Find the equation of the normal $N$ to circle $C$ at point $A$ .

[2]

(d)

Tangent $T$ and normal $N$ intersect the $y$ -axis at points $Q$ and $R$ respectively. Calculate the exact distance $QR$ .

[3]