Let a and b be non-zero real numbers. Then, the equation (a x^ 2 +b y^ 2 +c ) (x^ 2 -5 x…
Mathematics · JEE Main · NTA Exams — Co-ordinate Geometry
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,
- four straight lines, when c = 0 and a, b are of the same sign
- two straight lines and a circle, when a = b, 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
- 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
(B) two straight lines and a circle, when a = b, and c is of sign opposite to that of a
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