Question

Please help with math problem

Answer 1

`a_0 = -8`

`a_1=-6`

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

(1, 7)

(8, 6)

(7, -1).

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

For (1, 7)

`(1)^2 + (7)^2 + a_0(1) + a_1(7)=0`

`1 + 49 + a_0 + 7a_1=0`

`a_0 + 7a_1=-50` (1)

For (8, 6)

`(8)^2 + (6)^2 + a_0(8) + a_1(6)=0`

`64 + 36 + 8a_0 + 6a_1=0`

`8a_0 + 6a_1= -100` (2)

With these equations is enough to solve the system

`a_0 + 7a_1=-50` (1)

`8a_0 + 6a_1= -100` (2)

Multiply the equation (1) by -8 and add it to the equation (2)

`-8a_0 - 56a_1=400` (1)

`8a_0 + 6a_1= -100` (2)

-----------------------------------------------------

`-50a_1 = 300\\\\a_1 = -6`

Then

`a_0 + 7(-6) = -50\\\\a_0 = -50+42\\\\a_0=-8`

Finally the equation is:

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