NDA2019MathematicsThree Dimensional GeometryActual

What is the radius of the sphere x^2+y^2+z^2-6 x+8 y-10 z+1=0 ?

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Correct answer

C. 7

Step-by-step solution

The equation of sphere is x^2+y^2+z^2-6 x+8 y-10 z+1=0 Comparing the equation with general form of sphere, x^2+y^2+z^2+2 u x+2 v y+2 w z-d=0 aligned & we get, = -6 2 =-3, v= 8 2 =4, w= -10 2 =-5, d=1 & Radius = u^2+v^2+w^2-d & = (-3)^2+(4)^2+(-5)^2-1 & = 9+16+25-1 & = 49 =7 aligned

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