Question

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.

Solution

Correct option is

 

Let the centre of circle is (–h, –k) where, hk > 0. Since it touches x-axis

    

again (–h, –k) lies on – y – 1 = 0 then

             –h + k – 1 = 0            …(2)

Since the circle touches the line 4x – 3y + 4 = 0, so the length of perpendicular from (–h, –k) = radius of circle.   

 

From (2), k = h + 1

  

  

  

∴ Required equation of circle is [from (1)]   

                       

SIMILAR QUESTIONS

Q1

If the origin be one limiting point of a system of co-axial circles of whichx2 + y2 + 3x + 4y + 25 = 0 is a member, find the other limiting point.

Q2

Find the radical axis of co-axial system of circles whose limiting points are (–1, 2) and (2, 3).

Q3

Find the equation of the circle which passes through the origin and belongs to the co-axial of circles whose limiting points are (1, 2) and (4, 3).

Q4

Find the equation of the image of the circle x2 + y2 + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.

Q5

Find the area of the triangle formed by the tangents drawn from the point (4, 6) to the circle x2 + y2 = 25 and their chord of contact. Also find the length of chord of contact.

Q6

 

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

 

Q7

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

Q8

 

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.

Q9

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.

Q10

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.