Question: A circle, C, has equation x 2 + y 2 4x + 6y = 12 a. Show that the point A(5, 1) lies on

A circle, C, has equation x² + y² − 4x + 6y = 12

a. Show that the point A(5, 1) lies on C and find the centre and radius of the circle.

b. Find the equation of the tangent to C at point A. Give your answer in the form y = ax + b where a and b are rational numbers.

c. The curve y = x² − 2 intersects this tangent at points P and Q. Given that O is the origin, find, as a fraction in simplest form, the exact area of the triangle POQ.

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