Which of the following points lie on the parabola x2-4 a y -a x-a t2- y-2 a tb x-2 a t- y-a t2c x-2 a t2- y-a td x-2 a t- y-a t2

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

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Standard X

Mathematics

Straight Lines

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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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: 2at2=4aat2⇒4a2t2=4a2t2 Hence, (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.