Answer:
-5x + 4y = -11.
Step-by-step explanation:
If it's a circle then it must be x^2 not x.
x^2 + y^2 + 4x - 10y = 12
Using implicit differentiation:
2x + 2y y' + 4 - 10 y' = 0
y'( 2y - 10) = -2x - 4
y' = (-2x - 4)/(2y - 10)
y' = (-x - 2) / (y - 5) = the slope of the tangent.
At (3, 1), y' = (-3-2) / (1 - 5)
= 5/4.
So the required equation is
y - y1 = 5/4(x - x1) where x1 = 3 and y1 = 1.
y - 1 = 5/4(x - 3)
y = 5/4(x - 3) + 1
Multiply through by 4:
4y = 5(x - 3) + 4
4y = 5x - 15 + 4
In standard form the equation is:
-5x + 4y = -11.
