TS EAMCET · Maths · Three Dimensional Geometry
The equation of the sphere through the points \((1,0,0),(0,1,0)\) and \((1,1,1)\) and having the smallest radius
- A \(3\left(x^2+y^2+z^2\right)-4 x-4 y-2 z+1=0\)
- B \(2\left(x^2+y^2+z^2\right)-3 x-3 y-z+1=0\)
- C \(x^2+y^2+z^2-x-y+z+1=0\)
- D \(x^2+y^2+z^2-2 x-2 y+4 z+1=0\)
Answer & Solution
Correct Answer
(A) \(3\left(x^2+y^2+z^2\right)-4 x-4 y-2 z+1=0\)
Step-by-step Solution
Detailed explanation
Given points are \(A(1,0,0), B(0,1,0)\) and \(C(1,1,1)\) \(\begin{aligned} & A B=\sqrt{(0-1)^2+(1-0)^2+0^2}=\sqrt{2} \\ & B C=\sqrt{(0-1)^2+0^2+1^2-\sqrt{2}} \\ & C A=\sqrt{0^2+1^2+1^2}=\sqrt{2} \\ & \end{aligned}\) \(\therefore M A C\) is an equilateral triangle. \(\therefore\)…
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