Let d represent the distance from the center of the sphere x 2 + y 2 + z 2 − 6 x + 2 y = − 6 to the plane y = 2. Find two integer values of A so that the center of a second sphere x 2 + y 2 + z 2 + A y + 6 z = 2 is also d units from the plane y = 2.
A = and (Give the smaller one first.)

and  

Step-by-step explanation:

The given sphere is

This can be rearranged as

On comparing with the standard equation of a circle , with center and radius .

The center of the given circle is .

Now, as the perpendicular distance, , of a point from a plane is

.

[ as the given plane is y=2]

Similarly, the other equation of the circle, can be rearranged as

Here, the center for this circle is

From the given condition, the distance of the center from the plane is .

[from equation (i) ]

and

and  .

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

x = -5

step-by-step explanation: