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AP EAMCET20224 Jul 2022Evening ShiftMathematicsParabolaActual

Suppose a parabola passes through 0 , 4 , 1 , 9 and 4 , 5 and has its axis parallel to the y -axis. Then the equation of the parabola is

Options

  1. A19 x 2 + 12 y - 79 x - 48 = 0
  2. B19 x 2 + 12 y - 79 x + 48 = 0
  3. C19 y 2 + 12 x - 79 y - 48 = 0
  4. D19 y 2 + 12 x - 79 y + 48 = 0

Correct answer

A. 19 x 2 + 12 y - 79 x - 48 = 0

Step-by-step solution

Let the equation of parabola be y = a x 2 + b x + c Now given it passes through 0 , 4 ,   1 , 9   &   4 , 5 , Now on satisfying these points we get, 4 = 0 + 0 + c   . . . . . . . 1 9 = a + b + 4   . . . . . . 2   as   c = 4 5 = 16 a + 4 b + 4   . . . . . 3 Now solving equation equation 2   &   3 we get, a = - 19 12 ,   b = 79 12   &   c = 4 Now putting in the equation y = a x 2 + b x + c we get, 19 x 2 + 12 y - 79 x - 48 = 0

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