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Analytical Geometry> please answer as fast as possible if 4x-3...

question mark

please answer as fast as possible if 4x-3y =√3 is a tangent to a hyperbola 4x^2 - 9y^2 =1 then the eccentric angle of point of contact is
a)45
b)30
c)60
d)90
please give solution

Mrunal Sonawane , 6 Years ago

Grade 12

1 Answers

Karanveer

Answer is π/6

Step by Step Explanation :

Equation of given hyperbola can be written as

$\frac{x^{2}}{1/4} + \frac{y^{2}}{1/9} = 1$

So

$a^{2} = 1/4$

$a= 1/2$

Similarly $b= 1/3$

General point on ellipse $(1/2 \sec \theta,1/3 \tan \theta)$

Using T=0 on ellipse

We get

$4px-9qy = 1$

Where (p,q) is point of contact

Since it's equation of tangent, so by comparing this with given equation of tangent

$4x-3y = \sqrt{3}$

We get p= $1/\sqrt{3}$

And q = $1/3\sqrt{3}$

Since p = $1/2\sec \theta$

$1/2\sec \theta = 1/\sqrt{3}$

$sec\theta = 2/\sqrt{3}$

So $\Theta = π/6$ π/6

Hope it helps.

Last Activity: 6 Years ago

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