equation 2x-3y=10 touches the circle with centre m (-2,4)

Answer 1

the distance from (-2,4) to the line 2x-3y-10 = 0 is 2√13, so that's the radius of the circle.

(x+2)^2 + (y-4)^2 = 52

you can see this at

http://www.wolframalpha.com/input/?i=plot+%28x%2B2%29^2+%2B+%28y-4%29^2+%3D+52+and+2x-3y%3D10