one diameter of the circle circumscribing the rectangle ABCD is 4y=x+7 If the coordinates of A B are - Maths - Conic Sections

Question

one diameter of the circle circumscribing the rectangle ABCD is
4y=x+7 If the coordinates of A & B are (-3,4) &(5,4)
respectively , find the equation of the circle

ramandeep.singh · Accepted Answer

Centre P of the circle lies on the line $4 y = x + 7$ ...(1)

and perpendicular bisector of AB.

As AB is parallel to x-axis, therefore, perpendicular bisector of AB passes through $(\frac{- 3 + 5}{2}, \frac{4 + 4}{2}) = (1, 4)$ and is parallel to y-axis. So, its equation is

x = 1 ...(2)

On solving equations(1) and (2), we get

x = 1, y = 2.

Thus, the coordinates of centre P are (1, 2).

radius = AP = $\sqrt{(- 3 - 1)^{2} + (4 - 2)^{2}} = \sqrt{20}$

Hence, the equation of the circle is

$(x - 1)^{2} + (y - 2)^{2} = (\sqrt{20})^{2} \Rightarrow x^{2} + y^{2} - 2 x - 4 y - 15 = 0$

one diameter of the circle circumscribing the rectangle ABCD is 4y=x+7.If the coordinates of A & B are (-3,4) &(5,4) respectively , find the equation of the circle.