Math miscellaneousHard
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
x2 + y2 + z2 + 6x - 8y - 2z = 13 and
x2 + y2 + z2 - 10x + 4y - 2z = 8, then a equals
Options
A.- 1
B.1
C.- 2
D.2
Solution
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)
Mid point of centre is (1, 1, 1)
Satisfying this in the equation of plane, we get
2a - 3a + 4a + 6 = 0 ⇒ a = - 2.
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)
Mid point of centre is (1, 1, 1)
Satisfying this in the equation of plane, we get
2a - 3a + 4a + 6 = 0 ⇒ a = - 2.
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