Let $a$ and $b$ be non-zero real numbers. Then, the equation $$\left( a x ^ { 2 } + b y ^ { 2 } + c \right) \left( x ^ { 2 } - 5 x y + 6 y ^ { 2 } \right) = 0$$ represents (A) four straight lines, when $c = 0$ and $a , b$ are of the same sign (B) two straight lines and a circle, when $a = b$, and $c$ is of sign opposite to that of $a$ (C) two straight lines and a hyperbola, when $a$ and $b$ are of the same sign and $c$ is of sign opposite to that of $a$ (D) a circle and an ellipse, when $a$ and $b$ are of the same sign and $c$ is of sign opposite to that of $a$
Let $a$ and $b$ be non-zero real numbers. Then, the equation
$$\left( a x ^ { 2 } + b y ^ { 2 } + c \right) \left( x ^ { 2 } - 5 x y + 6 y ^ { 2 } \right) = 0$$
represents\\
(A) four straight lines, when $c = 0$ and $a , b$ are of the same sign\\
(B) two straight lines and a circle, when $a = b$, and $c$ is of sign opposite to that of $a$\\
(C) two straight lines and a hyperbola, when $a$ and $b$ are of the same sign and $c$ is of sign opposite to that of $a$\\
(D) a circle and an ellipse, when $a$ and $b$ are of the same sign and $c$ is of sign opposite to that of $a$