Question

Determine the equation of a circle centered at (0, 0) and through the point of cutting the line 3x + 4y = 24 with the x axis?

Answer 1

`x^2+y^2=64`

Explanation:

As the equation of `x`-axis i`y=0`, we can find the point of its intersection with the line `3x+4y=24` with the `x`-axis is obtained by putting `y-0`.

Then we have `3x+4xx0=24` or `3x=24` i.e. `x=8` and point of intersection is `(8,0)`.

As center is `(0,0)` and circle passes through `(8,0)`, its radius is `sqrt((8-0)^2+(0-0)^2)=sqrt64=8`

and hence equation of circle is

`(x-0)^2+(y-0)^2=8^2`

or `x^2+y^2=64`

graph{(x^2+y^2-64)(3x+4y-24)=0 [-16.83, 23.17, -9.36, 10.64]}