Question

If the equations of the two diameters of a circle are x – y = 5 and 2x + y = 4 and the

radius of the circle is 5, find the equation of the circle.
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Answer 1

Step-by-step explanation:

let the diameter of the circle be AB and LM respectively

x - y = 5...... 1 2x + y = 4..... 2

solving 1 and 2 , we get : x = 3 and y = -2

since the point intersection of two diameter of a circle is it's centre . therefore, coordinates of the centre of the required circle are ( 3 , -2) and it's radius is 5..

hence it's equation is

(x - 3 ) ^2 + ( y + 2 )^2 = 5^2. or x^2 + y^2 - 6x + 4y - 12 = 0