Question 36317: (a): Find the equation of the line joining the points
(─5, 2, 3) and (5, ─ 2, 3).
(b) Find the equation of the sphere, which contains the circle
x2 + y2 + z2 = 9, 3x + 3y + 3z = 5 and
passes through the origin.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! a): Find the equation of the line joining the points
(─5, 2, 3) and (5, ─ 2, 3).
EQN.IS GIVEN BY (X-X1)/(X2-X1)=(Y-Y1)/(Y2-Y1)=(Z-Z1)/(Z2-Z1)
(X+5)/(5+5)=(Y-2)/(-2-2)=(Z-3)/(3-3)
HENCE EQN.OF LINE IS
(X+5)/10=-(Y-2)/4 AND Z=3
4X+20=-10Y+20
4X+10Y=0 AND Z=3
(b) Find the equation of the sphere, which contains the circle
x2 + y2 + z2 = 9, 3x + 3y + 3z = 5 and
passes through the origin.
EQN. OF ANY SPHERE THROUGH ABOVE CIRCLE IS
(X^2+Y^2+Z^2-9)+K(3X+3Y+3Z-5)=0...IT PASSES THROUGH ORIGIN(0,0,0)..SO
-9-5K=0
K=-9/5
HENCE EQN.OF SPHERE IS BY SUBSTITITING FOR K AND SIMPLIFYING
5X^2+5Y^2+5Z^2-27X-27Y-27Z=0
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