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Question

If the curves 2x2+3y2=6 and ax2+4y2=4 intersect orthogonally then a=


A

2

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B

1

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C

3

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D

-3

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Solution

The correct option is A

2


Explanation for the correct option.

Step 1: Find the slope of the tangents

Given curves 2x2+3y2=6 and ax2+4y2=4 intersect orthogonally it means that their tangents are perpendicular.

The slope of the tangent to the curve, 2x2+3y2=6.

Differentiate with respect to x both sides we get:

4x+6ydydx=0dydx=-2x3y....(1)

The slope of the tangent to the curve, ax2+4y2=4.

Differentiate with respect to x both sides we get:

2ax+8ydydx=0dydx=-ax4y...(2)

Step 2: Find the value of a

We know that when two lines are perpendicular then the product of their slope is -1.

-2x3y-ax4y=-1ax26y2=-1x2y2=-6a

Substitute x2y2=-6ain any of the given equations to get:

a=2

Hence, option A is correct.


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