Table of Contents
Exit Questions
After doing the WeBWorK problems, come back to this page. The Exit Questions include vocabulary checking and conceptual questions. Knowing the vocabulary accurately is important for us to communicate. You will also find one last problem. All these questions will give you an idea as to whether or not you have mastered the material. Remember: the “Show Answer” tab is there for you to check your work!
Exit Questions
- Can you describe what a circle is using the words: center, radius and distance?
- How is the distance formula related to the Pythagorean Theorem?
- How can you recognize solutions to a quadratic equation in two variables as forming a line, a parabola, or a circle?
- What is the value of finding 4 points on the circle when graphing by hand?
- What is a perpendicular bisector?
- What information about a line is convenient to deal with if we want to write it’s equation in slope-intercept form?
- What about point-slope form?
$\bigstar$ Identify the center and the radius of the circle given by the equation
\[x^2 -4x +y^2+6y-23 =0.\]
Graph the circle and label four points on it.
Show Answer
$$x^2 -4x +y^2+6y-23 = 0 $$
$$x^2-4x + y^2+6y = 23 $$
$$x^2-4x + 4 + y^2+6y + 9 = 23 + 4+ 9$$
$$(x-2)^2+(y+3)^2 = 36$$
The center is $(2,-3)$. The radius is $\sqrt{36}=6$.
The points $(-4,-3)$, $(8,-3)$, $(2,3)$ and $(2,-9)$ are on the circle.
Need more help?
Don’t wait too long to do the following.
- Watch the additional video resources.
- Talk to your instructor.
- Form a study group.
- Visit a tutor. For more information, check the tutoring page.
