Question

The equation of the locus of a point whose distance from XY-plane is twice its distance from Z-axis is

• A. \( 2x^2 + 2y^2 - z^2 = 0 \)
• B. \( 2y^2 + 2z^2 - x^2 = 0 \)
• C. \( 4y^2 + 4z^2 - x^2 = 0 \)
• D. \( 4x^2 + 4y^2 - z^2 = 0 \)

Hint:

Memorize the formulas for distances in 3D space: - Distance from P(x,y,z) to XY-plane: \(|z|\) - Distance from P(x,y,z) to YZ-plane: \(|x|\) - Distance from P(x,y,z) to XZ-plane: \(|y|\) - Distance from P(x,y,z) to X-axis: \(\sqrt{y^2+z^2}\) - Distance from P(x,y,z) to Y-axis: \(\sqrt{x^2+z^2}\) - Distance from P(x,y,z) to Z-axis: \(\sqrt{x^2+y^2}\)

Answer 1

The Correct Option is D