#### Please Solve RD Sharma Class 12 Chapter15 Tangents and Normals Exercise Fill in the blanks Question 16 Maths Textbook Solution.

Points are $\left ( 0,0 \right )$  and  $\left ( 3,27 \right )$

Hint:

If the slope of tangent is equal to ordinate of point that means  $\frac{dy}{dx}=y$

Given:

The slope of tangent to curve  $y=x^{3}$  at a point is equal to ordinate of point.

To find:

We have to find the point

Solution:

We have,

$y=x^{3}$                                                                                                                                                … (i)

On differentiating with respect to $x$ , we get

$\frac{dy}{dx}=3x^{2}$                                                                                                                  $\left[\because \frac{d\left(x^{n}\right)}{d x}=n x^{n-1}\right]$

Now, we know that the given slope of tangent to the given curve at a point is equal to ordinate of point

$3x^{2}=y$                                                                                                                                               … (ii)

Putting value of  $y$ in equation (i), we get

$\Rightarrow$         $3x^{2}=x^{3}$

$\Rightarrow$     $x=3,0$  and  $y= 0,27$   [From equation (i)]

Thus the two points are  $\left ( 0,0 \right )$ and $\left ( 3,27 \right )$