NCERT Class 12-Mathematics: Chapter –6 Application of Derivatives Part 13
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Question 13:
Prove that the curves and touch each other.
Answer:
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.
Answer:
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 .
Answer:
We have,
And
And
And
From Eq.(i) and (ii),
So, the points of intersection are
For point
And
And for point