Question

Please help with math problem

Answer 1

Answer:

$a_0 = -6$

$a_1=8$

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

Step-by-step 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)

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

$36 + 6a_0=0$

$a_0 = -\frac{36}{6}\\\\a_0 = -6$

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:

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