JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q82

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MathematicsSingle correct+4 / -1Question 82 of 90

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of ΔABC is :

\dfrac1{x^2}+\dfrac1{y^2}+\dfrac1{z^2}=1

\dfrac1{x^2}+\dfrac1{y^2}+\dfrac1{z^2}=3

\dfrac1{x^2}+\dfrac1{y^2}+\dfrac1{z^2}=\dfrac19

\dfrac1{x^2}+\dfrac1{y^2}+\dfrac1{z^2}=9

Answer and worked solution

Official answer: A

The plane $\frac x\alpha+\frac y\beta+\frac z\gamma=1$ is 3 from O, so $\frac1{\alpha^2}+\frac1{\beta^2}+\frac1{\gamma^2}=\frac19$ . The centroid is $\left(\frac\alpha3,\frac\beta3,\frac\gamma3\right)$ ; substituting $\alpha=3x$ and so on,
$\frac1{x^2}+\frac1{y^2}+\frac1{z^2}=1.$

Topics:Equation of a plane

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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 82