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Question

If the curves x2a2+y212=1 and y3=8x intersect at right angles, then a2 is equal to :


A

16

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B

12

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C

8

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D

4

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E

2

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Solution

The correct option is D

4


Explanation for the correct option.

Step 1: Find the slopes of tangent

Given, curves x2a2+y212=1 and y3=8x intersect at right angles.

When two curves are at the right angle it means that their tangents are at a right angle.

For the slope of the tangent to the curve x2a2+y212=1 is:

2xa2+2y12dydx=0m1=-xa2×12y

For the slope of the tangent to the curve y3=8x is:

3y2dydx=8m2=83y2

Step 2: Find value of a2

m1·m2=-183y2-12xa2y=-132xa2y3=132x=a2y3a2=32xy3[y3=8x]a2=32x8xa2=4

Hence, option D is correct.


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