Alevel Maths Question

Find the equation of the normal to the circle
x^2 + y^2 - 4x +6y - 156 = 0
from the point (14,-8), and the tangent to the circle at the point (7,9).

what are your thoughts on this so far?

I have that the equation of the circle is (x-2)^2 + (y+3)^2 = 13^2 so the centre is (2,-3) and radius is 13 right? It might just be the wording of the question but I don't understand which coordinates I am supposed to use next.

I read the question as saying you have 2 points P and Q lying on the circle, and you need to find the equation of the normal through P and the tangent through Q, i.e. 2 separate independent tasks. I've just checked in my head that (14, -8 ) satisfies the equation of the circle, so you're just looking for the equation of a particular straight line in each case

I think I might have been reading the question wrong 😂
I've got y+8= (-5/12) (x-14) for the normal
And y-9= (12/5) (x-7) for the tangent

Your equation for the normal through (14,-8 ) is correct.

For the tangent through (7,9) your gradient is incorrect; you've worked out an equation for the normal through that point. So, since you have the gradient of the normal, what's the gradient of the tangent? And hence the equation of the tangent.

Oh right, so the gradient is -5/12. --> y-9=(-5/12)(x-7)