CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The eccentricity of the ellipse $$9{x^2} + 16{y^2} = 576$$ is


A
72
loader
B
54
loader
C
712
loader
D
74
loader

Solution

The correct option is D $${{\sqrt 7 } \over 4}$$

Consider the given ellipse.

$$9{{x}^{2}}+16{{y}^{2}}=576$$

$$ \dfrac{9{{x}^{2}}}{576}+\dfrac{16{{y}^{2}}}{576}=1 $$

$$ \dfrac{{{x}^{2}}}{64}+\dfrac{{{y}^{2}}}{36}=1 $$

$$ \dfrac{{{x}^{2}}}{{{8}^{2}}}+\dfrac{{{y}^{2}}}{{{6}^{2}}}=1 $$

 

We know that the general equation of the ellipse is,

$$\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1$$

 

On comparing, we get

$$a=8,b=6$$

 

We know that the eccentricity of the ellipse,

$$ e=\sqrt{1-\dfrac{{{b}^{2}}}{{{a}^{2}}}} $$

$$ e=\sqrt{1-\dfrac{36}{64}} $$

$$ e=\sqrt{\dfrac{28}{64}} $$

$$ e=\dfrac{\sqrt{7}}{4} $$


So, the value of the eccentricity is $$\dfrac{\sqrt{7}}{4}$$.


Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image