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AP EAMCET202316 May 2023Morning ShiftMathematicsParabolaActual

If a parabola having its axis parallel to X -axis passes through the points (0,-1),(6,1) and (-2,-3) , then the point at which this parabola cuts the X -axis is

Options

  1. A( 5 2 , 0 )
  2. B(-1,0)
  3. C(6,0)
  4. D( 8 5 , 0 )

Correct answer

A. ( 5 2 , 0 )

Step-by-step solution

Axis of parabola is x -axis. The equation of the parabola will of the form x=a y^2+b y+c ...(i) (0,-1),(6,1) and (-2,-3) passes through parabola (i), 0=a-b+c ...(ii) 6=a+b+c ...(iii) -2=9 a-3 b+c ...(iv) Solving eqns. (ii), (iii) and (iv), we get a= 1 2 ; b=3 and c= 5 2 Putting the above values in eqn. (i), we get x= 1 2 y^2+3 y+ 5 2 ...(5) For the point, at which parabola (v) cuts x -axis aligned & y=0 and x= 1 2 0+3 0+ 5 2 x= 5 2 & Point is ( 5 2 , 0 ) . aligned

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