Question

Find the equation of the circle passing through the origin and the points where the line 3x + 4y = 12 meets the axes of coordinates.

Answer 1

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 is given by

(x – x₁) (x – x₂) + (y – y₁) (y – y₂) = 0

(x – 0) (x – 4) + (y – 3) (y – 0) = 0

x² + y² – 4x – 3y = 0

∴The equation of the circle is x² + y² – 4x – 3y = 0