Question

The points on the curve 9y² = x³, where the normal to the curve makes equal intercepts with the axes are ………………

(A) (4, ±\(\frac{8}{3}\))

(B) (4, \(\frac{-8}{3}\))

(C) (4, + \(\frac{3}{8}\))

(D) (±4, \(\frac{8}{3}\))

Answer 1

Answer is (A)

We have the equation of the curve

9y² =x³   

We know that the slope of the tangent at a point on a given curve is given by  dy/dx

Now, the equation of normal with point (a,b) and  slope= -6b/a²  

It is given that  normal to the curve makes equal intercepts with the axes
Therefore,

point(a,b) also satisfy the given equation of the curve

Hence, The points on the curve  9y² = x³, where the normal to the curve makes equal intercepts with the axes are ( 4,±8/3)