Question

Please help with math problem

Answer 1

`a_0 = -6`

`a_1=8`

`x^2 +y^2 -6x + 8y = 0`

Explanation:

The equation of the circle has the following form

`x^2 + y^2 + a_0x + a_1y=0`

The equation of the circle has the following form

We know that the circle goes through the following points

(0, 0)

(6, 0)

(0, -8).

Then we substitute the values of x and y in the equation

For (0, 0)

`0^2 + 0^2 + a_0(0) + a_1(0)=0`

`0=0`

For (6, 0)

`6^2 + 0^2 + a_0(6) + a_1(0)=0`

`36 + 6a_0=0`

`a_0 = -(36)/(6)\\\\a_0 = -6`

For (0, -8)

`0^2 + (-8)^2 + a_0(0) + a_1(-8)=0`

`(-8)^2 - 8a_1=0`

`(-8)^2 = 8a_1`

`a_1=8`

Finally the equation is:

`x^2 +y^2 -6x + 8y = 0`