Correct Answer - Option 4 : x
2 + y
2 - 4x + 2y - 20 = 0
Concept:
The equation of the circle with centre at (h, k) and radius equal to a, is
(x - h)2 + (y - k)2 = a2
Calculation:
We have, the equations of the diameters as
x - y = 3 ----(1)
3x + y = 5 ----(2)
On solving equations (1) & (2), we get
x = 2 and y = -1
Since the point of intersection of any two diameters of a circle is its centre.
∴ Coordinates of the centre are (2, -1) and its radius is 5 (given).
So, Equation of the circle is given by
(x - 2)2 + (y + 1)2 = 52
⇒ x2 + 4 - 4x + y2 + 1 + 2y = 25
⇒ x2 + y2 - 4x + 2y - 20 = 0
Hence, the equation of the circle is x2 + y2 - 4x + 2y - 20 = 0.