Question:
Find the equation of the sphere having the centre (-2, 2, 3) and passing through the point (3, 4, -1).
Find the equation of the sphere having the centre (-2, 2, 3) and passing through the point (3, 4, -1).
Options:
- x2 + y2 + z2 + 4x + 4y + 6z – 28 = 0
- x2 + y2 + z2 + 4x – 4y – 6z + 28 = 0
- x2 + y2 + z2 + 4x + 4y + 6z + 28 = 0
- None of these
- x2 + y2 + z2 + 4x + 4y + 6z – 28 = 0
- x2 + y2 + z2 + 4x – 4y – 6z + 28 = 0
- x2 + y2 + z2 + 4x + 4y + 6z + 28 = 0
- None of these
Correct Answer: a)
Explanation:
i The equation of the sphere with centre (—2, 2, 3) is
‘ (+x2 + (y—x2+ (2-3) =r?
Radius, r = \/(3+2)2 + (4 —2)2 + (-1 3)? = 45
i .. Required equation of the sphere is
‘ (z+2)* + (y—2)* + (2 — 3) = (V5)? ‘
S24 y? +x244 —4y—62—28=0
i Condition for orthogonal ∩ion of two spheres is
‘ 2uiug + 2√1√9 + 2wiws = dy + ds
i The equation of the sphere with centre (—2, 2, 3) is
‘ (+x2 + (y—x2+ (2-3) =r?
Radius, r = \/(3+2)2 + (4 —2)2 + (-1 3)? = 45
i .. Required equation of the sphere is
‘ (z+2)* + (y—2)* + (2 — 3) = (V5)? ‘
S24 y? +x244 —4y—62—28=0
i Condition for orthogonal ∩ion of two spheres is
‘ 2uiug + 2√1√9 + 2wiws = dy + ds