Question

Length of the perpendicular from the centre of the ellipse $27x^{2} +9yx^{2} =243$ on a tangent drawn to it which makes equal intercepts on the coordinates axes is?

Answer 1

Answer:

Given ellipse is 16x

2

+9y

2

=144

⇒

9

x

2

+

16

y

2

=1

So tangent to the ellipse at any point

′

θ

′

is given by,

3

xcosθ

+

4

ysinθ

=1

∴x−intercept =

cosθ

3

and y−intercept =

sinθ

4

Now given both intercepts are equal ⇒

cosθ

3

=

sinθ

4

⇒tanθ=

3

4

∴sinθ=

5

4

and cosθ=

5

3

therefore required equation of the tangent is, x+y=5

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