Which of the following points lie on the parabola x2-4 ay-A- x-a t2- y-2 a tB- x-2 a t- y-a t2C- x-2 a t2- y-a tD- x -2 at - y - at 2

The correct option is D x=2at,y=at^2 Substituting x=2at,y=at^2 in the given equation (2at)^2=4a(at^2) ⇒ 4a^2t^2=4a^2t^2 Hence,(2at,at^2) lies on the parabola ...

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Standard XII

Mathematics

Position of a Point W.R.T Parabola

Which of the ...

Question

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

x= $a t^{2}$ ,y=2at

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x=2at ,y= $a t^{2}$

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x=2 $a t^{2}$ ,y=at

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x=2at,y= $a t^{2}$

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Solution

The correct option is D
x=2at,y= $a t^{2}$

Substituting x=2at,y= $a t^{2}$ in the given equation

$(2 a t)^{2} = 4 a (a t^{2})$

$\Rightarrow 4 a^{2} t^{2} = 4 a^{2} t^{2}$

Hence, $(2 a t, a t^{2})$ lies on the parabola $x^{2} = 4 a y$

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Similar questions

Q. Which of the following points lie on the parabola x² = 4ay?
(a) x = at², y = 2at
(b) x = 2at, y = at²
(c) x = 2at², y = at
(d) x = 2at, y = at²

Q. If

x = a t^{2}, y = 2 a t

then show that

\frac{d^{2} y}{d x^{2}} = \frac{- 1}{2 a t^{2}}

Q. Find

\frac{d^{2} y}{d x^{2}}

, of the following functions:

x = a t^{2}, y = 2 a t

Q. If

x = a t^{2}, y = 2 a t

then

\frac{d^{2} y}{d x^{2}} =

Q. If

x = a t^{2}, y = 2 a t

, then

\frac{d^{2} x}{d y^{2}} =

________.

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Which of the following points lie on the parabola x2=4ay?

The correct option is D x=2at,y=at2 Substituting x=2at,y=at2 in the given equation (2at)2=4a(at2) ⇒4a2t2=4a2t2 Hence,(2at,at2) lies on the parabola x2=4ay

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

The correct option is D
x=2at,y= $a t^{2}$

Substituting x=2at,y= $a t^{2}$ in the given equation

$(2 a t)^{2} = 4 a (a t^{2})$

$\Rightarrow 4 a^{2} t^{2} = 4 a^{2} t^{2}$

Hence, $(2 a t, a t^{2})$ lies on the parabola $x^{2} = 4 a y$