Question

Tangents are drawn from (6, 8) to the circle x2 + y2 = r2. Find the radius of the circle such that the areas of the âˆ† formed by tangents and chord of contact is maximum.

Solution

Correct option is

r = 5

 

Equation of chord of contact (QR) is 6x + 8y – r2 = 0  

  

                              

                     

   

  

                 

For maximum or minimum , then we get r = 5, (r ≠ 10 as P is outside the circle)  

SIMILAR QUESTIONS

Q1

 

Find the lengths of external and internal common tangents to two circlesx2 + y2 + 14x – 4y + 28 = 0 and x2 + y2 – 14x + 4y – 28 = 0.      

 

Q2

Find the lengths of common tangents of the circles x2 + y2 = 6x and x2 +y2 + 2x = 0.  

Q3

 

Find the equation of the circle circumscribing the triangle formed by the lines:

         x + y = 6, 2x + y = 4 and x + 2y = 5,

Without finding the vertices of the triangle.

Q4

Find the equation of the circle circumscribing the quadrilateral formed by the lines in order are 5x + 3y – 9 = 0, x – 3y = 0, 2x – y = 0, x + 4y – 2 = 0 without finding the vertices of quadrilateral.

Q5

Find the equation of a circle which touches the x-axis and the line 4x – 3y+ 4 = 0. Its centre lies in the third quadrant and lies on the line x – y – 1 = 0.

Q6

Find the equations of the circle which passes through the origin and cut off chords of length a from each of the lines y = x and y = –x.

Q7

Determine the radius of the circle, two of whose tangents are the lines 2x+ 3y – 9 = 0 and 4x + 6y + 19 = 0.

Q8

 

Find the equation of the circle which touches the circle

x2 + y2 – 6x + 6y + 17 = 0 externally and to which the lines

x2 – 3xy – 3x + 9y = 0 are normals.

Q9

 

Find the equation of a circle which passes through the point

(2, 0) and whose centre is the limit of the point of intersection of the lines 3x + 5y = 1and (2 + c)x + 5c2y = 1as c → 1.

Q10

Find the radius of smaller circle which touches the straight line 3x – y = 6 at (1, –3) and also touches the line y = x.