Question

Find the point on the curve 9y²=x³,where normal to the curve makes equal intercept with axe

Answer 1

Answer:

The normal to the curve has equal intercepts with both x and y axes at the point (4, 8/3)

Hope this helps.

Step-by-step explanation:

Differentiating

9y² = x³

=>  18y × dy/dx  =  3x²

=>  6y × dy/dx  =  x²

For the normal to the curve to have equal intercepts with both axes, the gradient of the normal must be -1.  Thus dy/dx = 1, so:

6y = x²

=> 36y² = x⁴ = x³x = 9y²x  =>  x = 4  ( we can divide by y because we can easily see that y = 0 is not a solution, so y ≠ 0 )

Finally,

6y = x²  =>  y = x² / 6 = 4² / 6 = 16 / 6 = 8 / 3