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Standard XII

Physics

Definite Integrals

The locus of ...

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

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

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

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

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None of these

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Solution

The correct option is D $3 x^{2} - y^{2} = 0$
By hypothesis,
$| O P | = 2 | P M |$
$\Rightarrow \sqrt{x_{1}^{2} + y_{1}^{2}} = 2 | x_{1} |$
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 $3 x^{2} - y^{2} = 0$ .

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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

The correct option is D $3 x^{2} - y^{2} = 0$
By hypothesis,
$| O P | = 2 | P M |$
$\Rightarrow \sqrt{x_{1}^{2} + y_{1}^{2}} = 2 | x_{1} |$
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 $3 x^{2} - y^{2} = 0$ .

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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

The correct option is D 3x2−y2=0By hypothesis, |OP|=2|PM|⇒√x21+y21=2|x1|On squaring both sides, we getx21+y21=4x21⇒3x21−y21=0∴ Locus of the point is 3x2−y2=0.

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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