circles help

i dont get what you mean, becuase ive reattempted this question and used y=-2/3x+c and subbed it into x^2-6x+9+y^2+6y+9=52
and i got x^2-6x+9+4x^2/9-4xc/3+c^2-4x+6c+9=52

This is very similar to the last question I helped you with. You need to group the x^2, x terms etc. like you did last time. Then use the discriminant.

im stuck on this bit because theres a c^2 in the equation and i dont know how to group it. like i know that im meant to factorise to get it in the form ax^2+bx+c where a is what i factorised but i dont know how to do it with the c^2

This is very similar to the last question I helped you with. You need to group the x^2, x terms etc. like you did last time. Then use the discriminant.

c^2 is a constant like 2 so group it with all the other numbers. So your ‘c’ could be something like

(c^2 + 5)

c^2 is a constant like 2 so group it with all the other numbers. So your ‘c’ could be something like

(c^2 + 5)

I gave the question a try;
You usually never need to expand the equation of a circle. Instead, since it tells you the gradient of the tangents, you can work out the gradient of the line that passes through the centre and the two tangents (perpendicular). Then you can use that equation to find the intersection and allowing you to complete the rest of the question.

I hope this was helpful

yeah thats how i ended up doing it at the end, because the first method i thought of didnt work. thanks !