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

(d) x = 2at, y = at2Substituting x = 2at, y = at2 in the given equation:2at2=4aat2 #8658;4a2t2=4a2t2Hence, (2at, at2) lies on the parabola x2 = 4ay. ...

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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 x² = 4ay?
(a) x = at², y = 2at
(b) x = 2at, y = at²
(c) x = 2at², y = at
(d) x = 2at, y = at²

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Solution

(d) x = 2at, y = at²

Substituting x = 2at, y = at² 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, (2at, at²) lies on the parabola x² = 4ay.

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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

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

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. If x = 2at, y = at², where a is a constant, then find

\frac{d^{2} y}{d x^{2}} at x = \frac{1}{2}

Q. If

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

at then

\frac{d y}{d x} =

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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

(d) x = 2at, y = at2Substituting x = 2at, y = at2 in the given equation:2at2=4aat2⇒4a2t2=4a2t2Hence, (2at, at2) lies on the parabola x2 = 4ay.

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

(d) x = 2at, y = at²

Substituting x = 2at, y = at² 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, (2at, at²) lies on the parabola x² = 4ay.