Which of the following can be the parametric equation of x 2-4 ayA- at -2- 2 at B- 2at- at 2 C- -2 a t- a t2D- at -2-2 at

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Parametric Equation of a Parabola

Which of the ...

Question

Which of the following can be the parametric equation of $x^{2} = 4 a y$

(at², 2at)

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(2at, at²)

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(-2at, at²)

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(at², -2at)

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Solution

The correct options are
B
(2at, at²)

C
(-2at, at²)

There can be more than one parametric representation of a given parabola. One condition is that it should be able to represent all points and should satisfy the curves equation.

So by substituting the given options, we get $B$ and $C$ as correct. That is $(2 a t, a t^{2})$ and $(- 2 a t, a t^{2})$ are parametric representations of $x^{2} = 4 a y$

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Similar questions

Match the following equation of parabola

$\begin{matrix} Parabola & parametric equation N) x^{2} = 4 a y & 1) (a t^{2}, 2 a t) E) y^{2} = 4 a x & 2) (- a t, 2 a t) W) y^{2} = - 4 a x & 3) (2 a t, a t^{2}) S) x^{2} = - 4 a y & 4) (2 a t, a t^{2}) \end{matrix}$

Which of the following points lie on the parabola $x^{2} = 4 a y ?$

Q. Find the area of tangle

A (a t_{1}^{2}, {2 a t}_{2}), B ({a t}_{2}^{2}, {2 a t}_{2}), C ({a t}_{3}^{2}, {2 a t}_{3})

Q. The curve described parametrically by

y = 2 a t

and

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Q. Find the equation of the tangent and the normal to the following curve at the indicated point.

x = \frac{2 a t^{2}}{1 + t^{2}}, y = \frac{2 a t^{3}}{1 + t^{2}}

t = 1 / 2

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Which of the following can be the parametric equation of x2 = 4ay

Which of the following can be the parametric equation of $x^{2} = 4 a y$