MHT CET · Maths · Circle
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 A circle and an ellipse, when \(a\) and \(b\) are of the same sign and \(c\) is of sign opposite to that of \(a\)
- B two straight lines and a hyperbola when \(a\) and \(b\) are of the same sign and \(c\) is of sign
- C Opposite to that of \(a\)
- D two straight lines and a circle, when \(a=b\) and \(c\) is of sign opposite to that of \(a\)
Answer & Solution
Correct Answer
(D) two straight lines and a circle, when \(a=b\) and \(c\) is of sign opposite to that of \(a\)
Step-by-step Solution
Detailed explanation
\(\because a=b\) 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.
\(\Rightarrow a x^2+b y^2+c=0\) 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.
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