Question

The locus of a point which moves in such a way that its distance from (0,0) is three times its distance from the x-axis, as given by.

• A. $x^{2} - 8y^{2} = 0$
• B. $x^{2} + 8y^{2} = 0$
• C. $4x^{2} - y^{2} = 0$
• D. $x^{2} - 4y^{2} = 0$

Answer 1

Answer: (A)

$x^{2} - 8y^{2} = 0$

Answer 2

Let the point be (x, y), then according to the given condition $\sqrt { x ^ { 2 } + y ^ { 2 } } = 3 y${distance from x-axis is y}

$\Rightarrow x ^ { 2 } + y ^ { 2 } = 9 y ^ { 2 } \Rightarrow x ^ { 2 } - 8 y ^ { 2 } = 0$.