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Chapter 10: Problem 78
Explain how to use \(y^{2}=8 x\) to find the parabola's focus and directrix.
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. Given the focus is at the pole, I can write the polar equation of a conic section if I know its eccentricity and the rectangular equation of the directrix.
How can you distinguish parabolas from other conic sections by looking at their equations?
Exercises 105鈥�107 will help you prepare for the material covered in the next section. Simplify and write the equation in standard form in terms of \(x^{\prime}\) and \(y^{\prime}\) $$ \left[\frac{\sqrt{2}}{2}\left(x^{\prime}-y^{\prime}\right)\right]\left[\frac{\sqrt{2}}{2}\left(x^{\prime}+y^{\prime}\right)\right]=1 $$
In Exercises \(61-66,\) find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. $$ \left\\{\begin{aligned} \frac{x^{2}}{4}+\frac{y^{2}}{36} &=1 \\ x &=-2 \end{aligned}\right. $$
How are the conics described in terms of a fixed point and a fixed line?
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