oints (1)
++z
8.
for
E
2
1
а
с
a
a
a
с
2
+ Z
y_2=0
х
2-
2
Find the equation of the sphere passing through (2, 0, 0),(0,2,0), (0.0,
(1, -5,2), (1, -3,0) and whose centre lies on the plane x+y+z=0.
having radius as small as possible. S
I 프
1. (1) 7 (x² + y2 +
(H.P.U. 2005; Pbi.U.
(ii) x² + y2 + 2
Prove that the equation to the sphere circumscribing the tetrahedron whos.
9.
(iv) x² + y2 + 2
are
(vi) x² + y2 + 2
x у
у
y = 0+ ,-
0,
= 1
3. x2 + y2 +2
z2
b
b
b
b c
2
x² + y² +
+ y
?
y z
Z
4.
is
a2 +62
+62 + c
2
a² +6² +6² a b c
OA, OB, OC are mutually perpendicular lines through the origin and
5. 3 (x² + y2 +2
10.
direction-cosines are <lı,mini >,< 12, m2, n2>, <l3 , M3, N3 >. If OA
7. (i) 3 (x + y
OB = b, OC = C, then find the equation of sphere through 0, A, B, C.
(ii) x² + y2 +
A sphere of constant radius k passes through the origin and meets the ai
11.
8. 3 (x² + y2 +
A, B, C. Prove that centre of the triangle ABC lies on a sphere.
10 x² + y2 + 2
A sphere of constant radius 2 k passes through the origin and meets the av
x² + y² +
12.
A, B, C. Show that the locus of the centroid of the tetrahedron OABC
16. x² + y² + z²
sphere x² + y2 + z2 = K?.
FET. Prove that
3.A plane passes through fixed point (a,h)and cuts the
dius of this circle
Coc) y
(H.P.U.2 15.
10 -
(G.N.D.U. 2005, 2007; P.U. 2
Answers
Answer:
oints (1)
++z
8.
for
E
2
1
а
с
a
a
a
с
2
+ Z
y_2=0
х
2-
2
Find the equation of the sphere passing through (2, 0, 0),(0,2,0), (0.0,
(1, -5,2), (1, -3,0) and whose centre lies on the plane x+y+z=0.
having radius as small as possible. S
I 프
1. (1) 7 (x² + y2 +
(H.P.U. 2005; Pbi.U.
(ii) x² + y2 + 2
Prove that the equation to the sphere circumscribing the tetrahedron whos.
9.
(iv) x² + y2 + 2
are
(vi) x² + y2 + 2
x у
у
y = 0+ ,-
0,
= 1
3. x2 + y2 +2
z2
b
b
b
b c
2
x² + y² +
+ y
?
y z
Z
4.
is
a2 +62
+62 + c
2
a² +6² +6² a b c
OA, OB, OC are mutually perpendicular lines through the origin and
5. 3 (x² + y2 +2
10.
direction-cosines are <lı,mini >,< 12, m2, n2>, <l3 , M3, N3 >. If OA
7. (i) 3 (x + y
OB = b, OC = C, then find the equation of sphere through 0, A, B, C.
(ii) x² + y2 +
A sphere of constant radius k passes through the origin and meets the ai
11.
8. 3 (x² + y2 +
A, B, C. Prove that centre of the triangle ABC lies on a sphere.
10 x² + y2 + 2
A sphere of constant radius 2 k passes through the origin and meets the av
x² + y² +
12.
A, B, C. Show that the locus of the centroid of the tetrahedron OABC
16. x² + y² + z²
sphere x² + y2 + z2 = K?.
FET. Prove that
3.A plane passes through fixed point (a,h)and cuts the
dius of this circle
Coc) y
(H.P.U.2 15.
10 -
(G.N.D.U. 2005, 2007; P.U. 2
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