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KVPY2011MathematicsParabola

The locus of the point P =( a , b ) where a , b are real numbers such that the roots of x ³+ ax ²+ bx + a =0 are in arithmetic progression is-

Options

  1. Aan ellipse
  2. Ba circle
  3. Ca parabola whose vertex in on the y -axis
  4. Da parabola whose vertex is on the x -axis

Correct answer

C. a parabola whose vertex in on the y -axis

Step-by-step solution

Let roots - d , , + d Sum 3 =- a =- a 3 product ( ²- d ² )=- a aligned pair product b &= ²- d+ ²+ d+ ²-d² ²-d²=3 b &=2 ²+3 & b-3= 2 9 a² locus x²= 9 2 (y-3) parabola aligned

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