## Question

### Solution

Correct option is

The required circle be x2 + y2 + 2gx + 2fy + c = 0.

Since (4, –1) lie on equation (1) so

17 + 8g – 2f + c = 0                 …(i)

Centre (–g, –f) lies on x = 2

So                                –g = 2

= –2

f = 1, c = 1.

#### SIMILAR QUESTIONS

Q1

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.

Q2

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

Q3

Find the equation of circle passing through the point of intersection of the circle x2 + y2 – 6x + 2y + 4 = 0 and x2 + y2 + 2x – 4y – 6 = 0 and whose centre lies on the line y = x.

Q4

Find the equation of the circle passing through the points of intersection of the circles x2 + y2 – 2x – 4y – 4 = 0 and x2 + y2 – 10x – 12y – 40 = 0.

Q5

Find the equation of circle through points of intersection of circle x2 + y2– 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x + 2y = 0.

Q6

Find the angle between the circles. S = x2 + y2 – 4x + 6y + 11 = 0 and

Q7

Find the equation of the system of circles coaxial with the circles.

x2 + y2 + 4x + 2y + 1 = 0, x2 + y2 – 2x + 6y – 6 = 0

Also find the equation of that particular circle whose centre lies on radical axis.

Q8

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

Q9

Find the circle whose diameter is the common chord of the circles

x2 + y2 + 2x + 3y + 1 = 0 and x2 + y2 + 4x + 3y + 2 = 0

S ≡ x2 + y2 + 2x + 3y + 1 = 0 S’ ≡ x2 + y2 + 4x + 3y + 2 = 0

Q10

Find the point of intersection of the line 2x + 3y = 18 and the circle x2 +y2 = 25.