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AP EAMCET202318 May 2023Evening ShiftMathematicsParabolaActual

A parabola having its axis parallel to Y -axis, passes through the points (0, 2 5 ),(4,-2) and (1, 8 5 ) ; Then a point that lies on this parabola is

Options

  1. A(3,5 / 2)
  2. B(-1,2)
  3. C(-2,28 / 5)
  4. D(2,8 / 5)

Correct answer

D. (2,8 / 5)

Step-by-step solution

Since, the axis of the parabola is parallel to y-axis. Then, (x-h)^2=4 a(y-k) Since, e q^ n (i) passes through the given points (0, 2 5 ) , (4,-2) & (1, 8 5 ) h ^2=4 a ( 2 5 - k ) (4-h)^2=4 a(-2-k) (1-h)^2=4 a ( 8 5 -k ) Solving eqn. (ii), (iii) & (iv), we get h = 3 2 , k = 7 4 , a =- 5 12 Putting above values in eqn. (i), we get (x- 3 2 )^2=- 5 3 (y- 7 4 ) Let's check the point (2, 8 5 ) on equation (v): 1 4 = 1 4 ; (2, 8 5 ) lies on the parabola.

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