find the equation of the tangent to the curve xy=c2 at a point (c/k,ck) on it - Maths - Application of Derivatives

Question

find the equation of the tangent to the curve xy=c2 at a
point (c/k,ck) on it

Neha Sethi · Accepted Answer

The equation of the given curve is xy=c2Differentiate it w
r t
x,we gety+xdydx=0⇒dydx=-yx⇒dydxck,ck=-ckck=-ck×kc=-k2The required equation of the tangent at ck,ck is⇒y-ck=-k2x-ck⇒y-ck=-k2xk-ck⇒y-ck=-xk2+ck⇒xk2+y-2ck=0