`P(x , y)` is a variable point on the parabola `y^2=4a x` and `Q(x+c ,y+c)` is another variable point, where `c` is a constant. The locus of the midpo

Question

`P(x , y)` is a variable point on the parabola `y^2=4a x` and `Q(x+c ,y+c)` is another variable point, where `c` is a constant. The locus of the midpo

`P(x , y)` is a variable point on the parabola `y^2=4a x` and `Q(x+c ,y+c)` is another variable point, where `c` is a constant. The locus of the midpoint of `P Q` is a/n parabola (b) hyperbola hyperbola (d) circle
A. parabola
B. ellipse
C. hyperbola
D. circle

Monjur Alahi

8 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A
(1) Let the midpoint of PQ be `(alpha,beta)`. Then,
`alpha=x+(c)/(2)andbeta=y+(c)/(2)`
`or(beta-(c)/(2))^(2)=4a(alpha-(c)/(2))`
`or(y-(c)/(2))^(2)=4a(x-(c)/(2))`
which is the required locus.

8 views Answered 2023-02-05 15:29