question_answer

Let O be the vertex and Q be any point on the parabola, \[{{x}^{2}}=8y.\]If the point P divides the line segment OQ internally in the ratio 1:3, then locus of P is : [JEE Main Solved Paper-2015 ]

A) \[{{y}^{2}}=2x\]                               

B) \[{{x}^{2}}=2y\]

C) \[{{x}^{2}}=y\]                 

D) \[{{y}^{2}}=x\]

Correct Answer: B

Solution :

Any point on the curve \[{{x}^{2}}=8y\]is \[(4t,2{{t}^{2}})\] Point P(h,x) divides the line segment joining OQ in ratio 1 : 3 \[\Rightarrow \]\[h=\frac{4t}{4}=t\And k=\frac{2{{t}^{2}}}{4}=\frac{{{t}^{2}}}{2}\] Hence locus of point P is \[{{x}^{2}}=2y\]