The sides of a square are x= 6, x =9, y = 3 and y = 6.
Find the equation of a circle drawn on di diagonal of the square as its diameter.

Open in App

Solution

Let the sies AB, BC, CD and DA of the square ABCD be represented by the equations
y = 3, x = 6, y = 6 and x = 9 respectively.
Then, coordinates are
A(6, 3), B(9, 3), C(9, 6) and D(6, 6)
The equation of the circle with diagonal AC
$(x - 6) (x - 9) + (4 - 3) (4 - 6) = 0 \Rightarrow x^{2} - 6 x - 9 x + 54 + y^{2} - 3 y - 6 y + 18 = 0 \Rightarrow x^{2} + y^{2} - 15 x - 9 y + 72 = 0$
The equation of the circle with diagonal BD as diameter is
$(x - 9) (x - 6) + (y - 3) (y - 6) = 0 \Rightarrow x^{2} - 9 x - 6 x + 54 + - 3 y - 6 y + 18 = 0 \Rightarrow x^{2} + y^{2} - 15 x - 9 y + 72 = 0 x^{2} + y^{2} - 15 x - 9 y + 72 = 0$

Suggest Corrections

Similar questions

Q. Find the equation of a circle drawn on the diagonal of the rectangle as its diameter, whose sides are along the lines

x = 5, x = - 2, y = 3

and

y = - 1

Q. Find the equation of the circle drawn on a diagonal of the rectangle as it diameter whose sides are

x + 1 = 0, y + 1 = 0, x - 4 = 0 a n d y - 2 = 0.

Find the equation of director circle of the circle whose diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area is 154 square units.

Q. The equation to the sides

A B, B C, C A

of a

△

are

x + y = 1; 4 x - y + 4 =

and

2 x + 3 y = 6

. Circle are drawn on

A B, B C, C A

as diameter. The point of concurrence of the common chord is

The equation of the circle which touches all the sides of the square with sides $y = 3, x = 6, y = 7$ and $x = 10$ is $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ . Find the value of $g + f + c$

Join BYJU'S Learning Program

The sides of a square are x= 6, x =9, y = 3 and y = 6. Find the equation of a circle drawn on di diagonal of the square as its diameter.

The sides of a square are x= 6, x =9, y = 3 and y = 6.
Find the equation of a circle drawn on di diagonal of the square as its diameter.