First slide

Parabola

Question

The centre $C$ of a variable circle passing through
a fixed point $(a, 0), a > 0$ , touches the line $y = x$ .
Locus of $C$ is a parabola whose directrix is

Moderate

A

$x + y = 0$
B

$x + y = a$
C

$x - y = 0$
D

$x - y = a$

Solution

$C$ is equidistant from the point $(a, 0)$ and the line
$y = x,$ so locus of $C$ is a parabola with directrix
$y = x$ i.e. $x - y = 0 .$

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