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MHT CET202211 Aug 2022Morning ShiftMathematicsCircleActual

Let a and b two non-zero real numbers. The equation (a x^2+b y^2+c ) (x^2-5 x y+6 y^2 ) Four straight lines, when c=0 and a, b are of the same sign.

Options

  1. AA circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a
  2. Btwo straight lines and a hyperbola when a and b are of the same sign and c is of sign
  3. COpposite to that of a
  4. Dtwo straight lines and a circle, when a=b and c is of sign opposite to that of a

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

a=b and c is of opposite sign 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 ' D ' is correct.

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