If 5{x^2} + λ {y^2} = 20 represents a rectangular hyperbola, then λ equals

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10-2. Parabola, Ellipse, Hyperbola

easy

If $5{x^2} + \lambda {y^2} = 20$ represents a rectangular hyperbola, then $\lambda $ equals

A

$5$

B

$4$

C

$-5$

D

None of these

Solution

(c) Since the general equation of second degree represents a rectangular hyperbola,

if $\Delta \ne 0,\,\,{h^2} > ab$ and

coefficient of ${x^2} + $ coefficient of ${y^2} = 0$.

Therefore the given equation represents a rectangular hyperbola,

if $\lambda + 5 = 0$ $i.e.$, $\,\lambda = – 5$.

Standard 11

Mathematics

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