First slide

Definition of a circle

Question

The locus of a point represented by $x = \frac{a}{2} (\frac{t + 1}{t}), y = \frac{a}{2} (\frac{t - 1}{t}),$ is

Moderate

A

an ellipse
B

a circle
C

a pair of lines
D

none of these

Solution

We have,
$\begin{aligned} x = \frac{a}{2} (\frac{t + 1}{t}), y = \frac{a}{2} (\frac{t - 1}{t}) \\ \Rightarrow \frac{2 x}{a} = 1 + \frac{1}{t}, \frac{2 y}{a} = 1 - \frac{1}{t} \end{aligned}$
$\Rightarrow \frac{2 x}{a} - 1 = \frac{1}{t}, 1 - \frac{2 y}{a} = \frac{1}{t}$
$\Rightarrow \frac{2 x}{a} - 1 = 1 - \frac{2 y}{a} \Rightarrow x + y = a_{r}$ which is a straight me.

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