CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the equation of the curve formed by the set of all those points the sum of whose distances from the points A(4, 0, 0) and B(-4, 0, 0) is 10 units.

Open in App
Solution

Let P(x, y, z) be an arbitrary point on the given curve.

Then,

PA+PB=10

(x4)2+y2+z2+(x+4)2+y2+z2=10

(x+4)2+y2+z2=10(x4)2+y2+z2 ...(i)

(x+4)2+y2+z2=100+(x4)2+y2+z220(x4)2+y2+z2 [On squaring both sides of (i)]

16x=10020(x4)2+y2+z2

5(x4)2+y2+z2=(254x)

25[(x4)2+y2+z2]=625+16x2200x

9x2+25y2+25z2225=0

Hence, the required equation of the curve is

9x2+25y2+25z2225=0.

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Conjugate of a Complex Number
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon