Correct Answer - Option 1 : x
2 + y
2 + z
2 + 4x – 6y – 8z = 7
Concept:
- General equation of a sphere cantered at the point (x0, y0, z0) with radius R is given by
- (x – x0)2 + (y – y0)2 + (z – z0)2 = R2
Calculation:
Given: Centre is at (-2, 3, 4) and radius is 6
⇒ (x0, y0, z0) = (-2, 3, 4) and R = 6
We know that general equation of sphere is (x – x0)2 + (y – y0)2 + (z – z0)2 = R2
⇒ (x – (-2)) 2 + (y – 3)2 + (z – 4)2 = 62
⇒ (x + 2) 2 + (y – 3)2 + (z – 4)2 = 62
⇒ x2 + 4x + 4 + y2 – 6y + 9 + z2 – 8z + 16 = 36
⇒ x2 + y2 + z2 + 4x – 6y – 8z + 29 = 36
⇒ x2 + y2 + z2 + 4x – 6y – 8z = 7
∴ Option 1 is correct.
