The coordinates of a moving point p are (2 t^2+4,4 t+6 ) . Then its locus will be a

Correct answer: (C) parabola. Hints: x=2 t^2+4, y=4 t+6, y=4 t+6 arrow t= ((y-6)/4 ) x=2 ((y-6)/4 )^2+4 ⇒ ((y-6)^2)/8=x-4 (y-6)^2=4(2)(x-4)

Q44 / 160 · WBJEE 2011 · Mathematics

The coordinates of a moving point \(p\) are \(\left(2 t^2+4,4 t+6\right)\). Then its locus will be a

A
circle
B
straight line
Correct answer
C
parabola
D
ellipse

Solution

Hints: \(x=2 t^2+4, y=4 t+6, \quad y=4 t+6 \rightarrow t=\left(\frac{y-6}{4}\right)\) \(\begin{aligned} & x=2\left(\frac{y-6}{4}\right)^2+4 \Rightarrow \frac{(y-6)^2}{8}=x-4 \\ & (y-6)^2=4(2)(x-4) \end{aligned}\)

Hence, the correct answer is option: 'C'.

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