Question -
Answer -
Given:
The line 3x + 4y = 12
The value of x is 0 on meeting the y – axis. So,
3(0) + 4y = 12
4y = 12
y = 3
The point is A(0, 3)
The value of y is 0 on meeting the x – axis. So,
3x + 4(0) = 12
3x = 12
x = 4
The point is B(4, 0)
Since the circle passes through origin and A and B
So, AB is the diameter
We know that the equation of the circle with AB as diameter isgiven by
(x – x1)(x – x2) + (y – y1) (y – y2) = 0
(x – 0) (x – 4) + (y – 3) (y – 0) = 0
x2 + y2 – 4x – 3y = 0
∴Theequation of the circle is x2 + y2 – 4x – 3y = 0