Question

consider the circle x^2+y^2-6x-8y=0, find its center and radius. then find the following:
a) find an equation of the tangent line to the circle at the point (0,0)
2) find an equation of the tangent line to the circle at point (6,0)
c) where do the two tangent lines intersect?

Answer 1

do you know how to find the center and radius?

Answer 2

general formula of a circle is
(x-a)^2 + (y-b)^2 = r^2
where a and b are x-coordinates of the circle and r = radius

Answer 3

so if you convert your equation to this form you can find centre and radius

Answer 4

can you do this?

Answer 5

you need to complete the square for x^2 - 6x and y^2 - 8y

Answer 6

can you help me with this?

Answer 7

I'll give you a hand with the x terms, then you can do the y terms by yourself.
We have x^2-6x on the left hand side. We need to get it in the form (x-a)^2, so we just need to factor it. The best way to do this in this example is completing the square, and we get:
(x-3)^2-9
Now if you do something similar for the y terms, you can keep the (x-3)^2 + (y-b)^2 on the left hand side and take all constants over to the right hand side to be your radius. (Note: The (x-3)^2 we have so far represents the x co-ordinate of the centre of the circle, which will be 3).
Please let me know if you need any more help.