TS EAMCET · Maths · Three Dimensional Geometry
The equation of the locus of a point whose distance from XY-plane is twice its distance from Z -axis is
- A \(2 x^2+2 y^2-z^2=0\)
- B \(2 y^2+2 z^2-x^2=0\)
- C \(4 y^2+4 z^2-x^2=0\)
- D \(4 x^2+4 y^2-z^2=0\)
Answer & Solution
Correct Answer
(D) \(4 x^2+4 y^2-z^2=0\)
Step-by-step Solution
Detailed explanation
Let the point be \( (x, y, z) \). Distance from XY-plane: \( |z| \) Distance from Z-axis: \( \sqrt{x^2+y^2} \) \( |z| = 2 \sqrt{x^2+y^2} \) \( z^2 = 4 (x^2+y^2) \) \( 4x^2+4y^2-z^2=0 \)
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