TS EAMCET · Maths · Three Dimensional Geometry
A variable plane is at a distance of 6 wits from the origin. If it meets the coordinate axes in \(A, B\) and \(C\), then the equation of the locus of the centroid of the \(\triangle A B C\) is
- A \(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{4}\)
- B \(x^2+y^2+z^2=4\)
- C \(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=1\)
- D \(\frac{1}{x^2}+\frac{1}{y^2}-\frac{1}{z^2}=\frac{1}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
Let the equation of plane \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\) Distance from origin is 6. \[ \therefore 6=\frac{1}{\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}} \Rightarrow \frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{1}{36} \] Centroid of plane is…
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