Equation x2+k1 y2+2 k2 y=a2 represents a pair of perpendicular straight lines if

Question

Equation x2+k1 y2+2 k2 y=a2 represents a pair of perpendicular straight lines if (A) k 1=1, k 2= a (B) k 1=1, k 2=- a (C) k 1=-1, k 2=- a (D) k 1=-1, k 2= a

Tardigrade Admin · Accepted Answer

Lines are perpendicular if 1+ k 1=0 Also for pair of straight line, ABC +2 FGH - AF 2- BF 2- CH 2=0 ⇒ k 1=-1 and k 2=± a

Q. Equation $x^{2} + k_{1} y^{2} + 2 k_{2} y = a^{2}$ represents a pair of perpendicular straight lines if

$k_{1} = 1, k_{2} = a$

$k_{1} = 1, k_{2} = - a$

$k_{1} = - 1, k_{2} = - a$

$k_{1} = - 1, k_{2} = a$

Lines are perpendicular if $1 + k_{1} = 0$
Also for pair of straight line,
$A BC + 2 FG H - A F^{2} - B F^{2} - C H^{2} = 0$
$\Rightarrow k_{1} = - 1$ and $k_{2} = \pm a$

Q. Equation x2+k1​y2+2k2​y=a2 represents a pair of perpendicular straight lines if

k1​=1,k2​=a

k1​=1,k2​=−a

k1​=−1,k2​=−a

k1​=−1,k2​=a