JEE Main · MathematicsHard

$Find the equation of the sphere which has its center at (1, 2, 3) and touches the plane $2x - y + 2z = 0$.$

Show correct answer & step-by-step solution

Correct answer: B — $(x - 1)^{2} + (y - 2)^{2} + (z - 3)^{2} = 4$

Solution

Radius r = \frac{∣2 ( 1 ) - 2 + 2 ( 3 ) ∣}{4 + 1 + 4} = \frac{6}{3} = 2 . The equation is (x - 1)^{2} + (y - 2)^{2} + (z - 3)^{2} = 2^{2} = 4 .

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