The equation of the circle described on the line joining the points (3, 4) and (2 ,-7 ) as diameter is ( x - 3) ( x - 2) + (y - 4) (y + 7) = 0 i.e `x^(2) + y^(2)- 5x + 3y - 22 = 0`.

If (x ,\ y) be on the line joining the two points (1,\ -3) and (-4,\ 2) , prove that x+y+2=0 .

The equation of the circle described on the common chord of the circles x^2 +y^2- 4x +5=0 and x^2 + y^2 + 8y + 7 = 0 as a diameter, is

If the middle point of the line segment joining (3, 4) and (k, 7) is (x, y) and 2x+2y+1=0 , find the value of k .

The equation of the circle passing through the point (1,1) and having two diameters along the pair of lines x^2-y^2-2x+4y-3=0 is a. x^2+y^2-2x-4y+4=0 b. x^2+y^2+2x+4y-4=0 c. x^2+y^2-2x+4y+4=0 d. none of these

The distance of the point (1,-2) from the common chord of the circles x^(2) + y^(2) - 5x +4y - 2= 0 " and " x^(2) +y^(2) - 2x + 8y + 3 = 0

Find the equation of the circle whose diameter is the common chord of the circles x^(2) + y^(2) + 2x + 3y + 1 = 0 and x^(2) + y^(2) + 4x + 3y + 2 = 0

Find the equation of the circle passing through the point (2, 4) and centre at the point of intersection of the lines x-y=4 and 2x+3y=-7 .

The equation of the circle having centre (0, 0) and passing through the point of intersection of the lines 4x + 3y = 2 and x + 2y = 3 is

The equation of the circle passing through (1/2, -1) and having pair of straight lines x^2 - y^2 + 3x + y + 2 = 0 as its two diameters is : (A) 4x^2 + 4y^2 + 12x - 4y - 15 = 0 (B) 4x^2 + 4y^2 + 15x + 4y - 12 = 0 (C) 4x^2 + 4y^2 - 4x + 8y + 5 = 0 (D) none of these

The equation of the medians of a triangle formed by the lines x+y-6=0, x-3y-2=0 and 5x-3y+2=0 is