JEE Main 2016 · 10 Apr · Shift 1 · Mathematics Q82

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MathematicsSingle correct+4 / -1Question 82 of 90

A hyperbola whose transverse axis is along the major axis of the conic, $\dfrac{x^2}3+\dfrac{y^2}4=4$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\dfrac32$ , then which of the following points does NOT lie on it ?

(0, 2)

(\sqrt5,\ 2\sqrt2)

(\sqrt{10},\ 2\sqrt3)

(5,\ 2\sqrt3)

Answer and worked solution

Official answer: D

The conic is $\frac{x^2}{12}+\frac{y^2}{16}=1$ , with foci $(0,\pm2)$ . The hyperbola is $\frac{y^2}4-\frac{x^2}{b^2}=1$ with $b^2=4\left(\frac94-1\right)=5$ . $(0,2)$ , $(\sqrt5,2\sqrt2)$ and $(\sqrt{10},2\sqrt3)$ satisfy $\frac{y^2}4-\frac{x^2}5=1$ ; $(5,2\sqrt3)$ gives $3-5=-2$ .

Topics:Hyperbola Ellipse

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JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 82