Question

Let a and b be non-zero and real numbers. Then, the equation (ax2 + by2 + c)(x2 - 5xy + 6y2) = 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 D 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

Answer 1

Correct option: (b) Two straight lines and a circle, when a = b and c is of sign opposite to that of a

Explanation:

Let a and b be non-zero real numbers.

Therefore the given equation

represent two straight lines passing through origin or ax2 + by2 + c = 0 when c = 0 and a and b are of same signs, then

which is a point specified as the origin.

When a = b and c is of sign opposite to that of a, ax2 + by2 + c = 0 represents a circle.

Hence, the given equation,

(ax2 + by2 + c)(x2 - 5xy + 6y2) = 0

may represent two straight lines and a circle.