Question

Locus of a point which moves such that its distance from the $X-axis$ is twice its distance from the line $x - y = 0$ is

• A. $x^2 + 4xy - y^2 = 0$
• B. $2x^2 - 4xy + y^2 = 0$
• C. $x^2 - 4xy + y^2 = 0$
• D. $x^2 - 4xy - y^2 = 0$

Answer 1

Answer: (B)

$2x^2 - 4xy + y^2 = 0$

Answer 2

$P_1 =$ length of perpendicular from P to x-axis.
$P_2 =$ length of perpendicular from p to y = x line.
$P_1 = 2P_2$
$\left|k\right| = 2.\frac{\left|h-k\right|}{\sqrt{2}}$
Squaring on both sides,
$k^2 =2(h-k)^2$
$k^{2}= 2h^{2} + 2k^{2} - 4hk$
$\Rightarrow 2h^{2} - 4hk + k^{2} = 0$
So, the locus of a point P is,
$2x^{2} - 4xy + y^{2} = 0$