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Question

The plane x+2y-z=4 cuts the sphere x2+y2+z2-x+z-2=0in a circle of radius


A

2

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B

2

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C

1

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D

3

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Solution

The correct option is C

1


Find the radius of the circle based on given information

Given, the plane x+2y-z=4 cuts the sphere x2+y2+z2-x+z-2=0

Center of sphere is 12,0,-12

So, radius of sphere is 122+02+-122+2=52

Now the perpendicular distance between centre of sphere of the given plane is given by,

d=12+20+12-412+22+(-1)2=36

Therefore, (Radiusofcircle)2=(Radiusofsphere)2-(Perpendiculardistance)2=52-96

Radiusofcircle=52-96

=30-1812=1212=1

Hence, option (C) is the correct answer.


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