Question

Show that the circles x^2+y^2-14x+2y-71=0, x^2+y^2-8x+10y+5=0 touch each other internally. Find the coordinates of the point of contact ?

Answer 1

Set x^2+y^2-14x+2y-71 = x^2+y^2-8x+10y+5
simplify and you will get one linear equation in x and y.

If the two curves touch each other they must have a common tangent that has the same slope for both curves. Do implicit differentiation of the two equations, find y' for each and equate the two. This will be the second equation in x and y.

Solve the two equations in two unknowns to get the point of contact.