NCERT Class 12-Mathematics: Chapter – 6 Application of Derivatives Part 13 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 13:

Prove that the curves and touch each other.

Given equation of curves are

And

And

And

And

And

Since, both the curves should have same slope.

Using the value of in , we get

For

And for

Thus, the required points of intersection are

For

And

For

And

Thus, for both the intersection points, we see that slope of both the curves are same.

Hence, the curves touch each other.

Question 14:

Find the co-ordinates of the point on the curve at which tangent is equally inclined to the axes.

Since, tangent is equally inclined to the axes.

From Eq. (i) ,

When

So, the required coordinates are

Question 15:

Find the angle of intersection of the curves and .

We have,

And

And

And

From Eq. (i) and (ii) ,

So, the points of intersection are

For point

And

And for point

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