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Question

Equation of the ellipse whose axes are the axes of coordinates and which passes through the point $$(-3,1)$$ and has eccentricity $$\sqrt{\dfrac25}$$ is 


A
3x2+5y232=0
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B
5x2+3y248=0
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C
3x2+5y215=0
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D
5x2+3y232=0
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Solution

The correct option is B $$3\mathrm{x}^{2}+5\mathrm{y}^{2}-32=0$$
Let the ellipse be $$\displaystyle \frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{b}^{2}}=1$$

It passes through $$(-3,1)$$ so $$\displaystyle \frac{9}{\mathrm{a}^{2}}+\frac{1}{\mathrm{b}^{2}}=1$$ ...(i) 

Also, $$\mathrm{b}^{2}=a^2(1-e^2)=\mathrm{a}^{2}(1-\dfrac25)$$

$$\therefore 5\mathrm{b}^{2}=3\mathrm{a}^{2}\ldots$$ (ii)

Solving we get $$\displaystyle \mathrm{a}^{2}=\frac{32}{3},\ \displaystyle \mathrm{b}^{2}=\frac{32}{5}$$

So, the ellipse is $$3\mathrm{x}^{2}+5\mathrm{y}^{2}=32$$.

Hence, option 'A' is correct.

Maths

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