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Provide Solution For R.D.Sharma Maths Class 12 Chapter 15 Tangents and Normals Exercise 15.1 Question 8 Maths Textbook Solution.

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Answer: $\text { The required point is }(0,0)$

Hint: $\text { The slope of the tangent is the limit of } \frac{\Delta y}{\Delta x} \text { as } \Delta x \text { approaches zero. }$

Given: $\text { The curve } y=x^{2}$

Solution: $y=x^{2}$

Differentiating the above with respect to $x$

$\therefore \frac{d}{d x}\left(x^{n}\right)=n x^{n-1}$

$\frac{d y}{d x}=2 x^{2-1}$

$\frac{d y}{d x}=2 x \quad \rightarrow(1)$

Also given the slope of tangent is equal to the x-coordinate

$\frac{d y}{d x}=x \quad \rightarrow(2)$

$\text { From (1)\&(2) we get }$

$2 x=x$

$x=0$

$\text { Substituting this in } y=x^{2}, \text { we get }$

$y=(0)^{2}$

$y=0$

$\text { So,the required point is }(0,0)$

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