Question

Help..medal will be awarded

Answer 1

Show that the circles \[x ^{2}+y ^{2}-16x-12y+75=0\] and \[5x ^{2}+5y ^{2}-32x-24y+75=0\] touch each other and find the equation of the common tangent at the point of contact.

I know how to show they touch each other, I just want to know how to find the equation of the common tangent at the point of contact

Answer 2

Do we get to use the calculus?

Answer 3

i think i got an equation for the tangent. I got y=-4x/3+(25/3)

Answer 4

i used calculus to differentiate one of the circle equations to find the gradient at (4,3)

Answer 5

see attached for graph

Answer 6

thank you