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

If a point P is moving such that the lengths of tangents drawn from P to the circles x2+y24x6y12=0 and x2+y2+6x+18y+26=0 are in the ratio 2:3 then find the equation of the locus of P.

Open in App
Solution

Equations of the circles are
S=x2+y24x6y12=0
S1=x2+y2+6x+18y+26=0
P(x1,y1) is any point on the locus and PT1, PT2 are the tangents from P to the two circles.
Given condition is

PT1PT2=23

3PT1=2PT2

3(x2+y24x6y12)=2(x2+y2+6x+18y+26)
3x2+3y212x18y36=2x2+2y2+12x+36y+52)
x2+y224x54y88=0

This is the locus of P(x1y1)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Parabola
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon