Question

Show that the quadrilateral formed by the straight lines x – y = 0, 3x + 2y = 5, x – y = 10 and 2x + 3y = 0 is cyclic and hence find the equation of the circle.

Answer 1

Solving the euations we get the coordinates of the quadrilateral.

Slope of AB = \(\frac{1-0}{1-0}\) =  1

Slope of CD = 1

AB||CD

Slope of BD = AC = - 1

AC||BD

So they form a rectangle with all sides = 90° 

The quadrilateral is cyclic as sum of opposite angles = 180° .

Now, AD = diameter of the circle equation of the circle with extremities A(0, 0)&D(6, - 4) is 

(x - 0)(x - 6) + (y - 0)(y + 4) = 0 

x² + y² – 6x + 4y = 0