Question

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.

Solution

Correct option is

x2 + y2 – 5x – 3y + 8 = 0

 

Let ABCD be a square and equation of its sides ABBCCD and DA arey = 1, x = 3, y = 2 and x = 2 respectively.

Then A = (2, 1), B = (3, 1), C = (3, 2) and D = (2, 2)

Since diagonals of squares are the diameters of the circle, then equation of circle is

          (x – 2) (x – 3) + (y – 1) (y – 2) = 0

⇒       x2 + y2 – 5x – 3y + 8 = 0 (If AC as diameter).

                                                      

 

SIMILAR QUESTIONS

Q1

Find the equation of that chord of the x2 + y2 = 15 which is bisected at (3, 2).

Q2

 

Find the centre and radius of the circle 

             2x2 + 2y2 = 3x – 5y + 7

Q3

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.

Q4

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

Q5

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).

Q6

 

Find the area of an equilateral triangle inscribed in the circle

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

Q7

 

Find the parametric form of the equation of the circle

                               x2 + y2 + px + py = 0

Q8

 

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.

Q9

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.

Q10

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