what is the greatest distance of the point P(10,7) from the circle x² + y² - 4x -2y -20 = 0 ?

max. distance of (10,7). from circle = distance of point (10,7) from centre of circle + radius of circle (i.e. distance of point through any diameter of circle)

For circle, x² + y² - 4x -2y -20 = 0 , centre is ( 2,1) i.e. (-g,-f))and radius / 2² + 1² - (-20) (i.e. /g²+f² - c) or /25 = 5

Since centre is (2,1) so distance of centre from (2,1) = / (10-2)² + (7 - 1)^{2 =} /64 + 36 = /100 = 10

So max distance = 10+ 5 = 15 units.