Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaGeneralMedium2 minPYQ_2011

MathematicsMediumsingle choice

Let $(x, y)$ be any point on the parabola $y^{2} = 4 x$ . Let $P$ be the point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $1 : 3$ . Then, the locus of $P$ is

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Solution:

$By section formula,$
$h = \frac{x + 0}{4}, k = \frac{y + 0}{4}$ $∴ x = 4 h$ and $y = 4 k$ Substituting in $y^{2} = 4 x$ , $(4 k)^{2} = 4 (4 h) \Rightarrow k^{2} = h$ or $y^{2} = x$ is required locus.

Stream:JEE_ADVSubject:MathematicsTopic:ParabolaSubtopic:General

⏱ 2mℹ️ Source: PYQ_2011

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