Introduction to Three Dimensional Geometry - Online Test

Answer : Option D
Explaination / Solution:

General equation of the sphere is x2+y2+z2+2gx+2fy+2hz+d=0---------------------1)

Since 1) passes through the point (0,0,0) using this in 1) we get d=0

Similarly 1) passes through ( a , 0 , 0 ) , ( 0 , b , 0 ) ( 0 , 0 , c ) using these values in 1)

a2+2ag=0=>a(a+2g)=0b2+2bf=0=>b(b+2f)=0c2+2ch=0=>c(c+2h)=0

But as abc≠0  So , a ≠0 ,b ≠0 ,c ≠0

So from above equations , we have a =  - 2g , b= - 2f , c = -2h

 centre is (-f ,-g , -h) = ( a/2 , b/2 , c/2 )

 

Answer : Option A
Explaination / Solution:

Since on Y axis x and z coordinate are 0 . So , Equations of Y axis are X=0 and Z=0

Answer : Option B
Explaination / Solution:

The equation  which represent generally YZ plane i.e. X=0 plane

Answer : Option B
Explaination / Solution:
No Explaination.

Answer : Option B
Explaination / Solution:

Yes , it is true because if we assume 2 sphere or more than that they wil coincide

Answer : Option B
Explaination / Solution:

Explanation:

 x + y = 0           (1)

 y + z = 0            (2)

x + z = 0             (3)

Subtracting 1 and 2 we get x-z=0   (4)

adding 3 and 4 we get x-0,y=0 and z=0

Answer : Option C
Explaination / Solution:
No Explaination.

Answer : Option B
Explaination / Solution:
No Explaination.

Answer : Option C
Explaination / Solution:

first degree equation in x, y, z can be written in the form Ax+By+Cz+d=0 Which represent a plane Where A,B and C are the direction ratios of normal to the plane

Answer : Option B
Explaination / Solution:
No Explaination.