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

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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