Question

Equation of locus of a point, such that its distance from the origin is one-third of the sum of its distance from co-ordinate axes, is ______

Options

• 4x² + 4y² - xy = 0

• 4x² - 8y² + xy = 0

• x² + y² - 3xy = 0

• 4x² + 8y² - xy = 0

Answer 1

Equation of locus of a point, such that its distance from the origin is one-third of the sum of its distance from co-ordinate axes, is 4x² + 4y² - xy = 0.

Explanation:

According to the given condition,

`sqrt(x^2 + y^2) = 1/3(y + x)`

Squaring both sides, we get

9(x² + y²) = (x + y)² ⇒ 4x² + 4y² - xy = 0.