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The radius of the circle in which the...

The radius of the circle in which the sphere `x^(I2)+y^2+z^2+2z-2y-4z-19=0` is cut by the plane `x+2y+2z+7=0` is a. `2` b. `3` c. `4` d. `1`

A

2

B

3

C

4

D

1

Text Solution

Verified by Experts

The correct Answer is:
b
Center of the sphere is (-1,1,2) and its radius `sqrt(1+1+4+19)=5`
CL, perpendicular distance of C from plane, is

`|(-1+2+4+7)/(sqrt(1+4+4))|=4`
Now, `AL^(2)=CA^(2)-CL^(2)=25-16=9`
Hence, radius of the circle `=sqrt9=3`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  4. The lines (x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1 are ...

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  5. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

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  6. Two systems of rectangular axes have the same origin. If a plane cu...

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  7. Find the equation of a plane which passes through the point (3, 2, 0...

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  12. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

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  13. The plane vecr cdot vecn = q will cotain the line vecr = veca + lambda...

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  14. The projection of point P(vecp) on the plane vecr.vecn=q is (vecs), th...

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  15. The angle between hati and line of the intersection of the plane vecr...

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  16. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

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  17. The equation of the plane which passes through the line of intersect...

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  18. Consider triangle A O B in the x-y plane, where A-=(1,0,0),B-=(0,2,0)a...

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  20. The co-ordinates of the point P on the line vecr =(hati +hatj + hatk...

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