The locus of a point which moves such that its distance from the point (0,0) is twice its distance from the Y-axis, is

Question

The locus of a point which moves such that its distance from the point (0,0) is twice its distance from the Y-axis, is (A) x2 − y2 = 0 (B) x2 − 3y2 = 0 (C) 3x2 − y2 = 0 (D) None of these

Tardigrade Admin · Accepted Answer

By hypothesis, | OP| = 2 |PM| <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e59d4face029acbc53f3bd1ca9772e2e-.png" /> ⇒ √x12+y12=2| x1| On squaring both sides, we get x12+y12=4 x12 ⇒ 3 x12-y12=0 ∴ Locus of the point is 3 x2-y2=0

Q. The locus of a point which moves such that its distance from the point $(0, 0)$ is twice its distance from the $Y$ -axis, is

$x^{2} - y^{2} = 0$

$x^{2} - 3 y^{2} = 0$

$3 x^{2} - y^{2} = 0$

None of these

By hypothesis,
$∣ OP ∣ = 2 ∣ PM ∣$

$\Rightarrow x_{1}^{2} + y_{1}^{2} = 2 ∣ x_{1} ∣$
On squaring both sides, we get
$x_{1}^{2} + y_{1}^{2} = 4 x_{1}^{2} \Rightarrow 3 x_{1}^{2} - y_{1}^{2} = 0$
$∴$ Locus of the point is $3 x^{2} - y^{2} = 0$

Q. The locus of a point which moves such that its distance from the point (0,0) is twice its distance from the Y-axis, is

x2−y2=0

x2−3y2=0

3x2−y2=0