The slope of the tangent to a curve at any point (x, y) on the curve is x divided by y. find the equation of the curve if the point (2, −3) is on the curve. x2 + y2 = 13 x2 + y2 = 25 x2 − y2 = −5 x2 − y2 = 5

The problem tells us that the slope of the tangent to a curve at any point on the curve is x divided by y, that is:

We also know that the point is on the curve. By taking a look on the options this point lies on both equations, namely:

We know that the derivative is the slope of the tangent line to the graph of the function at a given point. So taking the derivative of both equations we have:

And:

So also meets the requirement of the condition the slope of the tangent to a curve at any point (x, y) on the curve is x divided by y. Therefore this is the correct option.

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.

b

step-by-step explanation: