Question

# A point moves so that the sum of its distance from the points (4,0,0) and (âˆ’4,0,0) remain 10. The locus of the point is :

A
9x225y2+25z2=225
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B
9x225y225z2=225
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C
9x2+25y2+25z2=225
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D
9x225y2+25z2+225=0
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Solution

## The correct option is C 9x2+25y2+25z2=225Let the required point be (x,y,z)Given,Sum of distance of point from (4,0,0) and (−4,0,0) remains 10.√(x+4)2+y2+z2+√(x−4)2+y2+z2=10 ‘−(1)As we know that(x+4)2+y2+z2−[(x−4)2+y2+z2]=16x −(2)Divide eqs,(2) by (1)-∴(x+4)2+y2+z2−[(x−4)2+y2+z2]√(x+4)2+y2+z2+√(x−4)2+y2+z2=16x10⟹√(x+4)2+y2+z2−√(x−4)2+y2+z2=8x5 −(3)Adding eqs.(1) and (3)2√(x+4)2+y2+z2=10+8x5Squaring on both sides ⟹4[(x+4)2+y2+z2]=2500+64x2+800x25⟹100(x2+16+8x+y2+z2)=2500+64x2+800x⟹36x2+100y2+100z2−900=0⟹9x2+25y2+25z2=225Hence the locus of the point is 9x2+25y2+25z2=225

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