If (a - 2)x^2 + ay^2 = 4 represents a rectang | vedclass

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(C) The given equation is $(a - 2)x^2 + ay^2 = 4$.Dividing by $4$,we get $\frac{x^2}{\frac{4}{a-2}} + \frac{y^2}{\frac{4}{a}} = 1$.For a hyperbola,the

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(C) The given equation is $(a - 2)x^2 + ay^2 = 4$.Dividing by $4$,we get $\frac{x^2}{\frac{4}{a-2}} + \frac{y^2}{\frac{4}{a}} = 1$.For a hyperbola,the coefficients of $x^2$ and $y^2$ must have opposite signs. Let the equation be in the form $\frac{x^2}{A^2} - \frac{y^2}{B^2} = 1$ or $\frac{y^2}{A^2} - \frac{x^2}{B^2} = 1$.For a rectangular hyperbola,the magnitudes of the semi-axes must be equal,i.e.,$A^2 = B^2$.Here,the equation is $\frac{x^2}{\frac{4}{a-2}} - \frac{y^2}{-\frac{4}{a}} = 1$.Equating the denominators: $\frac{4}{a-2} = -\frac{4}{a}$.$a = -(a - 2)$.$a = -a + 2$.$2a = 2$.$a = 1$.

If $(a - 2)x^2 + ay^2 = 4$ represents a rectangular hyperbola,then $a$ equals:

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