Question

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

Answer 1

Answer:

so long question I am not able to answer

Answer 2

Equation of given hyperbola can be written as :

(x²)/1/4  +   (y²)/1/9 = 1

So,

a² = 1/4 => a = 1/2

b² = 1/9 => b = 1/3

General point on ellipse:

= 1/2secθ, 1/3tanθ

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 = √3

we get p = 1/√3 and q = 1/3√3

Since p = 1/2secθ

1/2secθ = 1/3√3

secθ = 2/√3

θ = 30

Hope this helps!