CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The equation of circle which passes through focus of parabola x2=4y and touches it at (6,9) is 
  1. x2+y2+24x27y+26=0
  2. x2+y2+48x12y+11=0
  3. x2+y2+18x22y+21=0
  4. x2+y2+18x28y+27=0


Solution

The correct option is D x2+y2+18x28y+27=0

dydx(6,9)=2x4=3
Equation of tangent : (y9)=3(x6)
3xy=9
Taking (6,9) as point on circle and line as equation of tangent, using the concept of family of circles
S+λL=0
(x6)2+(y9)2+λ(3xy9)=0     (1)
Required circle passes through (0,1).
36+64+λ(10)=0
λ=10
Putting λ=10 in (1), we get
(x6)2+(y9)2+10(3xy9)=0
x2+y2+18x28y+27=0

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More...



footer-image