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Question
If the plane 2ax−3ay+4az+6=0 passes through the midpoint of the line joining the centres of the spheres x2+y2+z2+6x−8y−2z=13 and x2+y2+z2−10x+4y−2z=8, then a equals
If the plane 2ax−3ay+4az+6=0 passes through the midpoint of the line joining the centres of the spheres x2+y2+z2+6x−8y−2z=13 and x2+y2+z2−10x+4y−2z=8, then a equals
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Solution
The correct option is C −2
Given plane 2ax−3ay+4az+6=0 passes through the mid point of the centre of spheres x2+y2+z2+6x−8y−2z=13 and x2+y2+z2−10x+4y−2z=8 respectively.
Centre of spheres are (−3,4,1) & (5,−2,1). So the mid point of centre is (1,1,1).
Now this point will satisfy equation of plane, 2a−3a+4a+6=0∴a=−2
Given plane 2ax−3ay+4az+6=0 passes through the mid point of the centre of spheres x2+y2+z2+6x−8y−2z=13 and x2+y2+z2−10x+4y−2z=8 respectively.
Centre of spheres are (−3,4,1) & (5,−2,1).
So the mid point of centre is (1,1,1).
Now this point will satisfy equation of plane, 2a−3a+4a+6=0
Now this point will satisfy equation of plane, 2a−3a+4a+6=0
∴a=−2
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