The radius of circle having maximum size passing through (2,4) and touching both the coordinate axes is- Answer is 10 please explain
The general equation of circle is (x-h)2 + (y-k)2 = R2
Here (h ,k ) are centre of the circle
But as the circle is touching both axes , so h = k = R
And the circle is passing through (2 ,4 )
Hence we have (2 - h)2 + (4-h)2 = h2
h2 -12h +20 = 0
Or (h-10)(h-2) = 0
But we have to consider the larger radius , so h = r = 10 is the required radius.