Let $a$ and $b$ two non-zero real numbers. The equation $\left(a x^2+b y^2+c\right)\left(x^2-5 x y+6…
Let $a$ and $b$ two non-zero real numbers. The equation
$\left(a x^2+b y^2+c\right)\left(x^2-5 x y+6 y^2\right)$
Four straight lines, when $c=0$ and $a, b$ are of the same sign.
A circle and an ellipse, when $a$ and $b$ are of the same sign and $c$ is of sign opposite to that of $a$
two straight lines and a hyperbola when $a$ and $b$ are of the same sign and $c$ is of sign
Opposite to that of $a$
two straight lines and a circle, when $a=b$ and $c$ is of sign opposite to that of $a$
Solution
$\because a=b$ and $c$ is of opposite sign
$\Rightarrow a x^2+b y^2+c=0$ will represent a circle $x^2-5 x y+6 y^2$ represent a pair of straight line passing through the origin
Hence, option ' $\mathrm{D}$ ' is correct.