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It seems like the image contains exercises asking to find the slope of the curve at a given point, specifically for equations that involve implicit differentiation. The answers for the slopes are provided as well. Let's go over how to approach solving problems like these, using implicit differentiation to find the slope.

For each exercise, we differentiate the given equation implicitly with respect to \( x \), and then substitute the coordinates of the given point to find the slope \( \frac{dy}{dx} \).

Would you like a detailed explanation of one of the exercises from the image? If so, feel free to choose an exercise number, and I can walk you through it.

Here are some related questions:
1. What is implicit differentiation and when is it used?
2. How do you compute the derivative of \( y \) with respect to \( x \) in implicit equations?
3. What is the geometrical significance of the slope of a curve at a point?
4. How do you apply the chain rule during implicit differentiation?
5. How does one find vertical tangents in implicitly defined curves?

**Tip:** Always remember to apply the chain rule when differentiating terms involving \( y \) with respect to \( x \), as \( y \) is treated as a function of \( x \).

In Exs. 27-37, find the slope of the curve at the given point for the equations provided, using implicit differentiation.

Explore how to use implicit differentiation to find the slope of a curve at specific points for equations like x^2 + y^2 - 12x + 4y - 5 = 0, x^2 + 2xy = x + 10, and others. This method involves key calculus concepts such as the chain rule and implicit differentiation.

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