Question

The circle x2 + y2 – 4x – 8y + 16 = 0 rolls up the tangent to it at  by 2 units, assuming the x-axis as horizontal, find the equation of the circle in the new position.  

Solution

Correct option is

 

Given circle is

           x2 + y2 – 4x – 8y + 16 = 0                …(1)

Let 

Equation of tangent to the circle (1) at P  is

  

Let A and B be the centres of the circles in old and new positions, then  

          

                                       (∵ AB makes an angle 60o with x-axis)

 

∴ Equation of the required circle is 

                      

SIMILAR QUESTIONS

Q1

 

Find the equation of the circle whose radius is 5 and which touches the circle 

              x2 + y2 – 2x – 4y – 20 = 0 at the point (5, 5).   

Q2

Find the locus of the mid point of the chord of the circle x2 + y2 = a2which subtend a right angle at the point (pq).

Q3

 

Let a circle be given by

                   2x (x – a) + y(2y – b) = 0            (a ≠ 0, b ≠ 0)

Find the condition on a and b if two chords, each bisected by the x-axis, can be drawn to the circle from (ab/2).

Q4

The centre of the circle S = 0 lie on the line 2x – 2y + 9 = 0 and S = 0 cuts orthogonally the circle x2 + y2 = 4. Show that circle S = 0 passes through two fixed points and find their co-ordinates.

Q5

 be a given circle. Find the locus of the foot of perpendicular drawn from origin upon any chord of Swhich subtends a right angle at the origin.

Q6

 be a given circle. Find the locus of the foot of perpendicular drawn from origin upon any chord of Swhich subtends a right angle at the origin.

Q7

P is a variable on the line y = 4. Tangents are drawn to the circle x2 + y2= 4 from P to touch it at A and B. The perpendicular PAQB is completed. Find the equation of the locus of Q.

Q8

 

Find the condition on abc such that two chords of the circle

                x2 + y2 – 2ax – 2by + a2 + b2 – c2 = 0  

passing through the point (ab + c) are bisected by the line y = x.  

Q9

 

Find the limiting points of the circles 

       (x2 + y2 + 2gx + c) + λ(x2 + y2 + 2fy + d) = 0

Q10

 

Find the equation of the circle of minimum radius which contains the three circles 

                   x2 – y2 – 4y – 5 = 0 

               x2 + y2 + 12x + 4y + 31 = 0  

and         x2 + y2 + 6x + 12y + 36 = 0