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Question

Find the equations of tangents to the ellipse
x225+y216=1
which are parallel to 3x+2y=25



A

3x + 2y = 17

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B

3x + 2y + 17 = 0

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C

3x + 2y + 32 = 0

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D

3x + 2y = 32

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Solution

The correct options are
A

3x + 2y = 17


B

3x + 2y + 17 = 0


Any line parallel to 3x + 2y = 25 can be written as 3x + 2y = k

We want to find the value of k. We can re - arrange
3x + 2y = k as y=32x+k2

Equation of tangent with Slope m to the ellipse
x2a2+y2b2=1 is given by y=mxa2m2+b2

Here

m=32  k2=25×(32)2+16

 k2=(5×32)2+16

=225+644

=2894

=172

 k=17

So the equation of tangents are 3x + 2y = 17 and 3x + 2y + 17 = 0


Mathematics

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