Question -
Answer -
Since the circle has intercept ‘a’ from x – axis, the circlemust pass through (a, 0) and (-a, 0) as it already passes through the origin.
Since the circle has intercept ‘b’ from x – axis, the circlemust pass through (0, b) and (0, -b) as it already passes through the origin.
Let us assume the circle passing through the points A(a,0) andB(0,b).
We know that the equation of the circle with AB as diameter isgiven by
(x – x1)(x – x2) + (y – y1) (y – y2) = 0
(x – a) (x – 0) + (y – 0) (y – b) = 0
x2 + y2 + ax + by = 0 or x2 + y2 –ax – by = 0
∴Theequation of the circle is x2 + y2 + ax + by = 0 or x2 + y2 –ax – by = 0