Suggested languages for you:

Americas

Europe

Problem 762

Find, both analytically and graphically, the points of intersection of the two curves whose equations are $$ 2 x+y-4=0 \text { and } y^{2}-4 x=0 $$

Expert verified

The points of intersection of the given curves are (1, 2) and (4, -4). This is determined analytically by solving the system of equations using the substitution method and then verifying graphically by plotting both equations on the same graph to observe their intersection points.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 43

Prove that if \(\mathrm{F}(0,1)\) is the focus, and the line \(\mathrm{y}=-1\) is the directrix, then the equation of the parabola is $\mathrm{y}=(1 / 4) \mathrm{x}^{2}$.

Chapter 43

Draw the graph of the curve whose equation is \(\mathrm{xy}=4\).

Chapter 43

Consider the equation \(x^{2}-4 y^{2}+4 x+8 y+4=0\) Express this equation in standard form, and determine the center, the vertices, the foci, and the eccentricity of this hyperbola. Describe the fundamental rectangle and find the equations of the 2 asymptotes.

Chapter 43

Show that if the pair of numbers \((\mathrm{x}, \mathrm{y})\) satisfies \(\mathrm{y}=(1 / 4 \mathrm{~d}) \mathrm{x}^{2}\), then the distance FP from \(\mathrm{F}(0, \mathrm{~d})\) to \(\mathrm{P}(\mathrm{x}, \mathrm{y})\) is equal to the distance \(\mathrm{PQ}\) from \(\mathrm{P}(\mathrm{x}, \mathrm{y})\) to \(\mathrm{Q}(\mathrm{x},-\mathrm{d})\).

Chapter 43

Graph the hyperbola \(y^{2}-x^{2}=4\). What are the equations of the asymptotes? Draw the asymptotes.

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner