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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
Plane 2ax−3ay+4az+6=0 passes through midpoint of the Joining the centres 1)x2+y2+z2+6x−8y−2z−13=0 centre (−3,4,1)2)x2+y2+z2−10x+4y−2Z−8=0 centre (5−2,1)so the mid point of centre will be (−3+52,4−22,1+12)=(1,1,1)from this point our plane is passing So ,2a(1)−3a(1)+4a(1)+6=0⇒3a+6=0⇒a=−63⇒a=−2Hence value of a will be −2
Plane 2ax−3ay+4az+6=0 passes through midpoint of the Joining the centres
1)x2+y2+z2+6x−8y−2z−13=0 centre (−3,4,1)
2)x2+y2+z2−10x+4y−2Z−8=0 centre (5−2,1)
so the mid point of centre will be (−3+52,4−22,1+12)
=(1,1,1)
from this point our plane is passing So ,2a(1)−3a(1)+4a(1)+6=0
⇒3a+6=0
⇒a=−63
⇒a=−2
Hence value of a will be −2
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