JEE Advance - Mathematics (1994 - No. 6)
Find the equation of such a curve passing through $$(0,k).$$
x = \pm \sqrt{k^2 - y^2} + C
x = \pm \int{\sqrt{k^2 - y^2}} dy + C
x = \pm \int{\frac{y}{\sqrt{k^2 - y^2}}} dy + C
x = \pm \int{\frac{dy}{\sqrt{k^2 - y^2}}} + C
x = \pm \int{\frac{dx}{\sqrt{k^2 - y^2}}} + C