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.

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