Question

The center of a circle is (−2,3) and a point on the circumference is (−5, −1)
(i) Find the equation of the line joining the two points (3 marks)
(ii) Show that the radius of the circle is 5 units (2 marks)
(iii) Write down the equation of the circle (1 mark)
(iv) Determine the equation of the tangent to the circle at the point (−5, −1) (3 marks)
(v) Find the points of intersection of the circle above with the circle
𝑥2 + 𝑦2 + 6𝑥 − 7𝑦 − 10 = 0

Answer 1

(i) the slope is (-1-3)/(-5+2) = -4/3 so y-3 = -4/3 (x+2)
(ii) the radius is r^2 = (-2+5)^2 + (3+1)^2 = 25
(iii) (x+2)^2 + (y-3)^2 = 25
(iv) the slope is -(x+2)/(y-3) = -3/4
(v) solve 𝑥^2 + 𝑦^2 + 6𝑥 − 7𝑦 − 10 = (x+2)^2 + (y-3)^2 - 25