<span>Let (x', y') be any point on the curve </span> <span>=> equation of the tangent at that point is </span> <span>y - y' = - (√y'/√x') (x - x') </span>
<span>x-intercept of this tangent is obtained by plugging y = 0 </span> <span>=> 0 - y' = - (√y'/√x') (x - x') </span> <span>=> x = √(x'y') + x' </span>
<span>y-intercept of the tangent is obtained by plugging x = 0 </span> <span>=> y - y' = - (√y'/√x') (0 - x') </span> <span>=> y = y' + √(x'y') </span>
<span>Sum of the x and y intercepts </span> <span>= √(x'y') + x' + y' + √(x'y') </span> <span>= (√x' + √y')^2 </span> <span>= (√c)^2 (because (x', y') is on the curve => √x' + √y' = √c) </span> <span>= c. hope this helps :D</span>