The equation of the locus of the point whose distance from y-axis is half the distance from origin is

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11th Standard Maths Two Dimensional Analytical Geometry

The equation of the locus of the point whose distance from y-axis is half the distance from origin is

Accepted Solution

3x²- y²= 0

Let the point be (x, y)
Its distance from origin is \(\sqrt{x^{2}+y^{2}}\)
Given \(x =\frac{1}{2} \sqrt{x^{2}+y^{2}} \)
\(\Rightarrow 2 x =\sqrt{x^{2}+y^{2}} \)
\(4 x^{2} =x^{2}+y^{2} \)
\(3 x^{2}-y^{2}=0 \) is the required equation of the locus

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The equation of the locus of the point whose distance from y-axis is half the distance from origin is

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