Question

Find the equation of the circum circle of the quadrilateral formed by the four lines ax + by ± c = 0 and bx – ay ± c = 0.

Solution

Correct option is

 

The given lines can be re-written as

                 ax + by + c = 0                 …(1)

                 ax + by + c = 0                  …(2)

                 bx ay + c = 0                  …(3)

                 bx – ay – c = 0                  …(4)

 

Equation (1) and (2) are parallel and equation (3) and (4) are also parallel.

                    

Since           m1m2 = –1 

Hence ABCD be a square and AC and BD are the diameters of the circle. After solving, we get

        

∴ Equation of circle is

           

SIMILAR QUESTIONS

Q1

 

Find the centre and radius of the circle 

             2x2 + 2y2 = 3x – 5y + 7

Q2

Find the equation of the circle whose centre is the point of intersection of the lines 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 and passes through the origin.

Q3

Find the equation of the circle concentric with the circle x2 + y2 – 8x + 6y– 5 = 0 and passing through the point (–2, –7).

Q4

A circle has radius 3 units and its centre lies on the line y = x – 1. Find the equation of the circle if it passes through (7, 3).

Q5

 

Find the area of an equilateral triangle inscribed in the circle

                       x2 + y2 + 2gx + 2fy + c = 0     

Q6

 

Find the parametric form of the equation of the circle

                               x2 + y2 + px + py = 0

Q7

 

If the parametric of form of a circle is given by

(i) x = – 4 + 5 cos θ and y = – 3 + 5 sin θ  

(ii) x = a cos α + b sin α and y = a sin α – b cos α

Find its Cartesian form.

Q8

Find the equation if the circle the end points of whose diameter are the centres of the circle x2 + y2 + 6x – 14y = 1 and x2 + y2 – 4x + 10y = 2.

Q9

The sides of a square are x = 2, x = 3, y = 1and y = 2. Find the equation of the circle drawn on the diagonals of the square as its diameter.

Q10

The abscissa of two points A and B are the roots of the equation x2 + 2ax – b2 = 0 and their ordinates are the roots of the equation x2 + 2px –q2 = 0. Find the equation and the radius of the circle with AB as diameter.