CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

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

A
9x225y2+25z2=225
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
9x225y225z2=225
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
9x2+25y2+25z2=225
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
9x225y2+25z2+225=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 9x2+25y2+25z2=225
Let 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+(x4)2+y2+z2=10 (1)

As we know that

(x+4)2+y2+z2[(x4)2+y2+z2]=16x (2)

Divide eqs,(2) by (1)-

(x+4)2+y2+z2[(x4)2+y2+z2](x+4)2+y2+z2+(x4)2+y2+z2=16x10


(x+4)2+y2+z2(x4)2+y2+z2=8x5 (3)


Adding eqs.(1) and (3)

2(x+4)2+y2+z2=10+8x5

Squaring on both sides

4[(x+4)2+y2+z2]=2500+64x2+800x25

100(x2+16+8x+y2+z2)=2500+64x2+800x

36x2+100y2+100z2900=0

9x2+25y2+25z2=225

Hence the locus of the point is 9x2+25y2+25z2=225


flag
Suggest Corrections
thumbs-up
0
mid-banner-image
mid-banner-image
similar_icon
Related Videos
thumbnail
lock
De-Moivre's Theorem
MATHEMATICS
Watch in App