Question

I will mark as brainliest. Please Help.

Answer 1

Answer:

y = $\frac{-5}{12}$ 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: $y-y_1=m(x-x_1)$, where (x_1, y_1) is the point and m is the slope. So, we have:

y - 12 = $\frac{-5}{12}$ (x - 12)

We can then solve for y (if you want): y = $\frac{-5}{12}$ x +17.

Hope this helps!

Answer 2

Answer:

12y + 5x = 169

Step-by-step explanation:

Differentiate wrt x

2x + 2y(dy/dx) = 0

dy/dx = -x/y

At (5,12)

m = -5/12

y = (-5/12)x + c

12 = -25/12 + c

c = 169/12

y = (-5/12)x + 169/12

12y + 5x = 169