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AP EAMCET20225 Jul 2022Morning ShiftMathematicsParabolaActual

Which of the following represents a parabola?

Options

  1. Ax=4 t, y=4 t
  2. Bx^2-2=-2 t, y= ^2 ( t 2 )
  3. Cx = t, y = t
  4. Dx= 1- t , y= ( t 2 )+ ( t 2 )

Correct answer

B. x^2-2=-2 t, y= ^2 ( t 2 )

Step-by-step solution

From option (a). aligned & x=4 t, y=4 t & x^2=16 ^2 t, y^2=16 ^2 t aligned So, x^2+y^2=16 , so this equation of a circle. From option (b), x^2-2=-2 t, y= ^2 ( t 2 )x^2=2-2 t ...(i) y= 1+ t 2 ...(ii) From Eq. (ii), t=2 y-1 Now, x^2=2-2 t aligned & x^2=2-2(2 y-1) x^2=2-4 y+2 & x^2=4-4 y aligned So, this is represent the parabola.

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