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  • Let    be any point on the parabola <img alt="y^{2}=4x" src="https://entrancecorne

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

Option: 1

x^{2}=y


Option: 2

y^{2}=x


Option: 3

y^{2}=2x


Option: 4

x^{2}=2y


Answers (1)

best_answer

By section formula,

h=\frac{x+ 0}{4} \,\, ,k=\frac{y+0}{4}

\therefore x=4h \, ,y=4k

Substituting in y^{2}=4x\, \, ,

\begin{aligned} & \Rightarrow(4 k)^2=4(4 h) \\ \Rightarrow & k^2=h \\ \Rightarrow & y^2=x \text { is required locus. } \end{aligned}

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Ritika Harsh

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