1A few good observations reduce this problem to a sitter !
The given straight line : - h x + k y = 2 h k
The given circle : - ( x - k ) 2 + ( y - h ) 2 = c 2
Observations : -
1 . The given straight line passes through the center of the circle .
2 . This indicates that the given line is , in fact , " a diameter " of the given circle .
3 . Since the lines joining Origin to the point of intersection of the line and the circle are at right angles , hence , Origin must lie on the cirle , so that the line ( which is proven to be a diameter ) and Origin are parts of a semicircle .
4 . Now that we know origin lies on the circle , let us put " ( 0 , 0 ) " in the equation of the circle .
Voila !!!!!!!!!!!!!! Eureka !!!!!!!!!!!!!!
h 2 + k 2 = c 2