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