## Question

### Solution

Correct option is

(1, 2)

Since the radical centre of three circles described on the sides of a triangle as diameters is the orthocenter of the triangle.

Given sides are            4x – 7y + 10 = 0                           …(1)

x + y – 5 = 0                                …(2)

7x + 4y – 15 = 0                           …(3)

Since lines (1) and (3) are perpendicular the point of intersection of (1) and (3) is (1, 2), the orthocenter of the triangle. Hence radical centre is (1, 2).

#### SIMILAR QUESTIONS

Q1

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.

Q2

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

Q3

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 and whose radius is 4.

Q4

Find the equation of the circle through points of intersection of the circlex2 + y2 – 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x+ 2y = 0.

Q5

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.

Q6

Find the angle between the circles

Q7

Find the equation of the circle which cuts the circle x2 + y2 + 5x + 7y – 4 = 0 orthogonally, has its centre on the line x = 2 and passes through the point (4, –1).

Q8

Find the equations of the two circles which intersect the circles

x2 + y2 – 6y + 1 = 0 and x2 + y2 – 4y + 1 = 0

Orthogonally and touch the line 3x + 4y + 5 = 0.

Q9

Find the radical centre of circles x2 + y2 + 3x + 2y + 1 = 0,

x2 + y2 – x + 6y + 5 = 0 and x2 + y2 + 5x – 8y + 15 = 0. Also find the equation of the circle cutting them orthogonally.

Q10

Find the co-ordinates of the limiting points of the system of circles determined by the two circles

x2 + y2 + 5x + y + 4 = 0 and x2 + y2 + 10x – 4y – 1 = 0