Radius parametric equation represented by x=2 a (1-t^2 1+t^2 ), y… - Vidyadip

MCQ

Radius parametric equation represented by $x=2 a\left(\frac{1-t^2}{1+t^2}\right), y=\frac{4 a t}{1+t^2}$ is

A
$a$
B
$a ^2$
C
3a
✓
2a

✓

Answer

Correct option: D.

2a

(D)
$x=2 a\left(\frac{1-t^2}{1+t^2}\right)$ ...(i)
$y=\frac{4 at }{1+ t ^2}$ ...(ii)
Squaring and adding (i) and (ii), we get
$x^2+y^2=4 a ^2 \cdot \frac{\left(1- t ^2\right)^2}{\left(1+ t ^2\right)^2}+\frac{16 a ^2 t ^2}{\left(1+ t ^2\right)^2}$
$=\frac{4 a^2}{\left(1+t^2\right)^2}\left[1-2 t^2+t^4+4 t^2\right]$
$=\frac{4 a^2}{\left(1+t^2\right)^2}\left(1+t^2\right)^2$
$\therefore \quad x^2+y^2=(2 a)^2$
$\therefore \quad$ Radius $=2 a$

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