Coordinate Geometry

Question 1

How to find the equation of a tangent of a circle

Answer 1

Use the centre of the circle and the point where the tangent meets the circle to find the gradient of the radius.
Find the negative reciprocal of that - this is the gradient of the tangent.
Substitute the coordinates where the tangent and circle meet and the gradient of the tangent into y-y₁ = m (x-x₁)
Rearrange into the order you want

Question 2

Federico’s formula for finding the equation of a tangent of a circle

Answer 2

Where x₁ and y₁ are coordinates of the point where the tangent meets the circle and r is the radius of the circle:

(xx₁) + (yy₁) = r²