Question

Find the equations of the circles drawn on the diagonals of the rectangle as its diameter whose sides are `x=6, x=-3, y=3 a n d y=-1.`

Answer 1

Let ABCD be the given rectangle and let its sides AD, BC, AB and CD be represented by the equations ` x = - 3, x = 6, y = - 1 and y = 3 ` respectively.
Then, the coordinates of A and C are
`A(-3, - 1 ) and C(6, 3)`.
So, the equation of the circle with AC as diameter is given by
`" " (x + 3 ) ( x - 6) + (y + 1 )( y - 3) = 0`
` rArr x ^(2) + y ^(2) - 3x - 2y - 21 = 0`