If 5 x^2 + y^2 = 20 represents a rectangular hyperbola, then equa… - Vidyadip

MCQ

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

A
$5$
B
$4$
✓
$-5$
D
None of these

✓

Answer

Correct option: C.

$-5$

c
(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 $\lambda + 5 = 0$ $i.e.$, $\,\lambda = - 5$.

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