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

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 (A) -1 (B) 1 (C) -2 (D) 2

Tardigrade Admin · Accepted Answer

Plane 2ax - 3ay + 4az + 6 = 0 passes through the mid point of the centre of spheres

x^{2} + y^{2} + z^{2} + 6 x - 8 y - 2 z = 13

and

x^{2} + y^{2} + z^{2} - 10 x + 4 y - 2 z = 8

respectively centre of spheres are (- 3, 4, 1) and (5, - 2, 1). Mid point of centres is (1, 1, 1).
Satisfying this in the equation of plane, we get
2a - 3a + 4a + 6 = 0

\Rightarrow

a = -2.

Q. 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

-1

1

-2

2

Q. If the plane 2ax - 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres $x^{2} + y^{2} + z^{2} + 6 x - 8 y - 2 z = 13$ and $x^{2} + y^{2} + z^{2} - 10 x + 4 y - 2 z = 8$ then a equals