Find the y-intercept of the graph x^2 - 10x + y^2 - 10y + 25 = 8x + 4y + 16. Write your answer as an ordered pair.
The y axis intercept occurs when x = 0 so put x = 0 into the equation and solve for y value
y^2 -10y + 25 = 4y + 16
y^2 -14y +9 = 0
If you use the quadratic formula to find y = two roots so the equation of the circle intersects the y -axis at two points....
y= 7 +- 2 sqrt (10) and x = 0 for each of the points
+130071 Not as tough as it seems
x^2 - 10x + y^2 - 10y + 25 = 8x + 4y + 16 simplify as
x^2 -10x - 8x + y^2 - 10y -4y + 25 - 16 = 0
x^2 - 18x + y^2 - 14y + 9 = 0
x^2 -18x + y^2 -14y = -9 complete the square on x and y
x^2 -18x + 81 + y^2 - 14y + 49 = -9 + 81 + 49
(x - 9)^2 + ( y - 7)^2 = 121
To find the y intercept, let x = 0
(0 - 9)^2 + ( y -7)^2 = 121
81 + ( y -7)^2 = 121
(y -7)^2 = 121 -81
(y - 7)^2 =40 take both roots
y - 7 = ± sqrt (40) = ± 2sqrt (10)
So ....two y intercepts
y = (0, 7 - 2sqrt (10) )
And
y = (0, 7 + 2sqrt (10) )
