Question

Examine if the two circles x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally.

Solution

Correct option is

Internally

 

Given circles are

                      x2 + y2 – 2x – 4y = 0                       …(1)

and                x2 + y2 – 8y – 4 = 0                         …(2)

let centres and radii of circles (1) and (2) are represented by C1r1 andC2r2 respectively.    

  

   

   

   

   

                        

Hence the two circles touch each other internally.

SIMILAR QUESTIONS

Q1

 

Find the condition that chord of contact of any external point

(hk) to the circle x2 + y2 = a2 should subtend right angle at the centre of the circle.

Q2

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 = y2 = c2. Show that abc are in GP.

Q3

Find the equation of the chord x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

Q4

Find the middle point of the chord intercepted on line lx + my + n = 0 by the circle x2 + y2 = a2.

Q5

Find the locus of middle points of chords of the circle x2 + y2 = a2, which subtend right angle at the point (c, 0).

Q6

Find the equations of the tangents from the point A(3, 2) to the circle x2y2 + 4x + 6y + 8 = 0 .

Q7

If two tangents are drawn from a point on the circle x2 + y2 = 50 to the circle x2 + y2 = 25 then find the angle between the tangents.

Q8

 

Find the equation of the diameter of the circle

x2 + y2 + 2gx + 2fy + c = 0 which corresponds to the chord ax = by + d= 0.

Q9

Find the locus of the pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.

Q10

 

Find the equation of the circle passing through (1, 1) and the points of intersection of the circles

x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0.