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For the ellipse \mathrm{ 4 x^2+5 y^2-16 x-30 y+60=0} which is true? 

Option: 1

Centre is (2,3)
 


Option: 2

Length of major axis is 1
 


Option: 3

\mathrm{e=\frac{1}{\sqrt{5}}}
 


Option: 4

All of these


Answers (1)

best_answer

The given equation can be written as

\mathrm{ \begin{aligned} & 4(x-2)^2+5(y-3)^2=1 \\\\ & \Rightarrow \quad \frac{(x-2)^2}{1 / 4}+\frac{(y-3)^2}{1 / 5}=1(a>b) \end{aligned} }
So, centre is (2,3)

Length of major axis \mathrm{=2 \times \frac{1}{2}=1}

Length of minor axis \mathrm{=2 \times \frac{1}{\sqrt{5}}=\frac{2}{\sqrt{5}}}

Now, \mathrm{e=\sqrt{1-\left(\frac{2}{\sqrt{5}}\right)^2} \Rightarrow e=\frac{1}{\sqrt{5}}}

Posted by

Shailly goel

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