Consider the spheres `x^2+y^2+z^2-4y+3=0 and x^3+y^2+z^2+2x+4z-4=0`.
Consider the following statements :
1. The two spheres intersect each other.
2. The radius of first sphere is less than that of second sphere.
Which of the above statements is/are correct?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

C

Explanation

`x^2+y^2+z^2-4y+3=0`
`x^2+y^2-4y+4-4+z^2+3=0`
`x^2+(y-2)^2+z^2=1`
Sphere with centre (0,2,0) and radius 1 unit.
`x^2+y^2+z^2+2x+4z-4=0`
`x^2+2x+1-1+y^2+z^2+4z+4-4-4=0`
`(x+1)^2+y^2(z+2)^2=3^2`
Sphere with centre (-1,0,-2) and radius 3 units.
`r_1+r_2=3+1=4`
`C_1C_2ltr_1r_2`
`:." Two spheres inersect each other"`.