If 5x^2 + lambda y^2 = 20 represents a rectan | vedclass

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(C) The standard equation of a hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ or $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$.Given the equation $5x^

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$-5$

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(C) The standard equation of a hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ or $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$.Given the equation $5x^2 + \lambda y^2 = 20$,we can rewrite it as $\frac{x^2}{4} + \frac{\lambda y^2}{20} = 1$.For this to represent a hyperbola,the coefficients of $x^2$ and $y^2$ must have opposite signs.For a rectangular hyperbola,the equation must be of the form $x^2 - y^2 = a^2$ or $xy = c^2$.In the general form $Ax^2 + By^2 = C$,the condition for a rectangular hyperbola is $A + B = 0$.Here,$A = 5$ and $B = \lambda$.Therefore,$5 + \lambda = 0$,which gives $\lambda = -5$.

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

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