CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Two tangents are drawn from (1,2) to the circle x2+y28x+6y+20=0. Which of the following is false ?
  1. angle between the tangents is π2
  2. equation of one of the two tangents is x2y5=0
  3. one of the two tangents passes through the origin
  4. sum of the squares of the slopes of the two tangents is 154


Solution

The correct option is D sum of the squares of the slopes of the two tangents is 154
For the given circle, C=(4,3),r=5
Let the equation of any tangent be
y+2=m(x1)
mxy(m+2)=0   ...(1)

Applying condition for tangency,
|4m+3(m+2)|m2+1=5
(3m+1)2=5(m2+1)
2m2+3m2=0
m1=12, m2=2
(m1,m2 are the slopes of two tangents)

m1m2=1
Angle between the tangents is π2
Equation of tangents are x2y5=0 and 2x+y=0 (from (1))
2x+y=0 is passing through the origin.
m21+m22=174

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
QuestionImage
QuestionImage
View More...



footer-image