MATHS QUESTION HELP: Core 2

I can do 19 (a), I just need help on 19 (b) and (c)! Thank you

I can do 19 (a), I just need help on 19 (b) and (c)! Thank you

for b)

differentiate w.r.t x the equation of the circle with implicit differentiation
and arrange to y'

for c)

the equation of the tangent line in (x0, y0) point of the circe
$y-y_0=m(x-x_0)$

when m=y'(x0,y0)

For (b), if you know the centre O of the circle, think about a radius OP joining the centre to the point.

What's the gradient of this radius line in terms of x, y and the coordinates of the circle?

How does the gradient of the tangent at P relate to the gradient of the radius OP?

For b) I got 4-x/y-8

c) y - 8 = 4-x/y-8 (x-21)

y^2 - 16y + 64 = -x^2 + 25x -84

Where did I got wrong? :/

You're making this much too difficult for yourself!

The gradient of the tangent is (4-x)/(y-8) as you say. At the point (21, 8) you have y-8 = 0 so the gradient of the tangent is undefined. So what sort of line is the tangent at that point? So what is the equation of the tangent at that point?

Why is y-8=0?

At the point (21, 8), x = 21 and y = 8. So y - 8 = 0