Question

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

Solution

Correct option is

Internally

 

  

   

  

    

  

So the touch each other internally.

SIMILAR QUESTIONS

Q1

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

Q2

 

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 lows of the point P.   

Q3

 

Find the length of tangents drawn from the point (3, – 4) to the circle

     2x2 + 2y2 – 7x – 9y – 30 = 0   

Q4

 

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. 

Q5

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 thouchese x2 + y2 = e2 find ab in.

Q6

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

Q7

Find the equation of the tangents from the point A(3, 2) to the circle x2 +y2 + 4x + 6y + 8 = 0.

Q8

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

Q9

Find the equation of diameter of the circle x2 + y2 + 2gx + 2fy + c = 0 which corresponds o the chord ax + by + λ = 0. 

Q10

 

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

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