Question

If $x^2+\alpha y^2+2\beta y=a^2$ represents a pair of perpendicular straight lines, then

• A. $\alpha =1,\beta =a$
• B. $\alpha =1,\beta =-a$
• C. $\alpha =-1,\beta =-a$
• D. $\alpha =-1,\beta =a$

Answer 1

Answer: (C), (D)

$\alpha =-1,\beta =-a$
$\alpha =-1,\beta =a$

Co-efficient of $x^2+$Co-efficient of $y^2=0$
$\Rightarrow 1+\alpha =0$
$\therefore \alpha =-1$
Also, $△=0$
$1.\alpha .\left({-a}^2\right)+0-1.{\beta }^2-0-0=0$
$\therefore {\beta }^2=-\alpha .a^2$
$\therefore \beta =\pm a$
Hence, $\alpha =-1,\beta =\pm a$