The correct option is B Two straight lines and a circle, when a=b and c is of sign opposite to that of a
Let a and b non-zero real numbers.
Therefore the given equation
(ax2+by2+c)(x2−5xy+6y2)=0 implies either
x2−5xy+6y2=0
⇒ (x−2y)(x−3y)=0
⇒ x=2y
And x=3y
Represent two straight lines passing through origin or ax2+by2+c=0 when c=0 and a and b are of same signs, then
ax2+by2+c=0x=0
And y=0
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.