wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the locus of a point which moves in such a way that the sum of its distances from(4,3) and (4,1) is 5.

Open in App
Solution

Let the moving or variable point be P(x,y) and the given points be A(4,3) and B(4,1)
By the conditions of the problem,
PA+PB=5
PA=5PB
(x4)2+(y3)2=5(x4)2+(y1)2
(x4)2+(y3)2=25+(x4)2+(y1)210(x4)2+(y1)2
y26y+9=25+y22y+110(x4)2+(y1)2
10(x4)2+(y1)2=4y+17
Squaring both sides again
100(x28x+16+y22y+1)=(4y+17)2
100(x2+y28x2y+17)=16y2+136y+284
100x2+100y216y2800x200y136y+1700284=0
100x2+84y2800x336y+1411=0

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Definition and Standard Forms
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon