Answer:
y = [tex]\frac{-5}{12}[/tex] x +17
Step-by-step explanation:
We'll have to use calculus and differentiating to solve this.
Differentiate the given equation with respect to x:
x^2 + y^2 = 169
2x + 2y * (dy/dx) = 0
Solve for dy/dx:
dy/dx = -x/y
Now, what this derivative means is actually the slope of the tangent line at the point (x, y).
Substituting 5 in for x and 12 in for y, we get:
dy/dx = -5/12
So, the slope is -5/12
Now, we have a slope (m = -5/12) and a point (5,12), so we can write an equation in point-slope form, which is: [tex]y-y_1=m(x-x_1)[/tex], where (x_1, y_1) is the point and m is the slope. So, we have:
y - 12 = [tex]\frac{-5}{12}[/tex] (x - 12)
We can then solve for y (if you want): y = [tex]\frac{-5}{12}[/tex] x +17.
Hope this helps!
