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let the eccentricity of the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ be reciprocal to that of the ellipse $x^{2} + 4 y^{2} = 4 .$ if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is $\frac{x ^{2}}{3} - \frac{y ^{2}}{2} = 1$ (b) a focus of the hyperbola is $(2, 0)$ (c) the eccentricity of the hyperbola is $\frac{5}{3}$ (d) the equation of the hyperbola is $x^{2} - 3 y^{2} = 3$

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let the eccentricity of the hyperbola

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

be reciprocal to that of the ellipse

x^{2} + 4 y^{2} = 4 .

if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is

\frac{x ^{2}}{3} - \frac{y ^{2}}{2} = 1

(b) a focus of the hyperbola is

(2, 0)

\frac{5}{3}

(d) the equation of the hyperbola is

x^{2} - 3 y^{2} = 3

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Question Text	let the eccentricity of the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ be reciprocal to that of the ellipse $x^{2} + 4 y^{2} = 4 .$ if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is $\frac{x ^{2}}{3} - \frac{y ^{2}}{2} = 1$ (b) a focus of the hyperbola is $(2, 0)$ (c) the eccentricity of the hyperbola is $\frac{5}{3}$ (d) the equation of the hyperbola is $x^{2} - 3 y^{2} = 3$
Answer Type	Video solution: 1
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