CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The eccentricity of the conic $$4(2y-x-3)^{2}-9(2x+y-1)^{2}=80$$ is :


A
2
loader
B
133
loader
C
12
loader
D
132
loader

Solution

The correct option is A $$\dfrac{\sqrt{13}}{3}$$
The given equation can also be written as $$4\left(\dfrac{2y - x - 3}{\sqrt{5}}\right)^2 - 9\left(\dfrac{2x + y - 1}{\sqrt{5}}\right)^2 = 16$$
Let $$X = \dfrac{2y - x - 3}{\sqrt{5}}$$ and $$Y = \dfrac{2x + y - 1}{\sqrt{5}}$$
$$4X^2 - 9Y^2 = 16$$
$$\Rightarrow \dfrac{X^2}{4} - \dfrac{Y^2}{\dfrac{16}{9}} = 1$$
Now $$b^2 = a^2(e^2 - 1)$$
So, $$\dfrac{16}{9} = 4(e^2 - 1) $$
$$\Rightarrow e = \dfrac{\sqrt{13}}{3}$$
Hence, option 'B' is correct.

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image