Question

Find the equation of the tangents to the circle x2 + y2 = 16 drawn from the point (1, 4).

Solution

Correct option is

8x + 15y = 68

 

Given circle is

                               x2 + y2 = 16

any tangent of (1) in terms of slope is 

                        

Which passes through (1, 4)

  

  

From (2), equations of tangents drawn from (1, 4) are  

                  

or 8x + 15y = 68 respectively.

SIMILAR QUESTIONS

Q1

Find the co-ordinates of the middle point of the chord which the circlex2 + y2 + 4x – 2y – 3 = 0 cuts off the line x – y + 2 = 0.

Q2

For what value of λ will the line = 2x + λ be a tangent to the circle x2 +y2 = 5?

Q3

Find the equation of tangent to the circle x2 + y2 – 2ax = 0 at the point   

Q4

Find the equation of the tangents to the circle x2 + y2 = 9, which  Are parallel to the line 3x + 4y – 5 = 0

Q5

 

Find the equation of the tangents to the circle x2 + y2 = 9, which

Are perpendicular to the line 2x + 3y + 7 = 0.

Q6

Find the equation of the tangents to the circle x2 + y2 = 9, which make an angle of 60o with the x-axis.

Q7

Show that the line 3x – 4y = 1 touches the circle x2 + y2 – 2x + 4y + 1 = 0. Find the co-ordinates of the point of contact.

Q8

The line (x – 2) cos θ + (y – 2) sin θ = 1 touches a circle for all values of θ. Find the circle.

Q9

 

Find the equation of the normal to the circle

x2 + y2 – 5x + 2y – 48 = 0 at the point (5, 6).

Q10

The angle between a pair of tangents from a point P to the circle x2 + y2+ 4x – 6y + 9 sin2α + 13 cos2α = 0 is 2α. Find the equation of the locus of the point P.