Inequalities And Systems Of Inequalities In Two Variables Sketch t...

Inequalities And Systems Of Inequalities In Two Variables Sketch the graph of the solution set to the system of inequalities below. 1. 𝟐𝒙 + 𝟑𝒚 ≥ −𝟔 𝒚 − 𝟐𝒙 < −𝟒 Sketch the graph of the solution set to the nonlinear system of inequalities below. 2. 𝒙 𝟐 + 𝒚 𝟐 < 𝟗 𝒚 ≥ 𝒙 − 𝟏 The Parabola 3. Consider the following parabola below. 𝒚 = − 𝟏 𝟒 (𝒙 − 𝟐) 𝟐 + 𝟒 a. Write the parabola below in the form (𝒙 − 𝒉) 𝟐 = 𝟒𝒑(𝒚 − 𝒌). b. Find the vertex of the parabola. c. Find the focus of the parabola d. Find the directrix of the parabola e. Graph the parabola, making sure to include its vertex, focus, and directrix. 4. Consider the following parabola below. 𝒙 = 𝒚 𝟐 + 𝒚 − 𝟐 a. Write the parabola below in the form (𝒚 − 𝒌) 𝟐 = 𝟒𝒑(𝒙 − 𝒉). b. Find the vertex. c. Find the focus. d. Find the directrix. e. Graph the parabola, making sure to include its vertex, focus, and directrix. The Ellipse And The Circle 5. Consider the following ellipse below. 𝟗𝒙 𝟐 + 𝟗𝟎𝒙 + 𝟐𝟓𝒚 𝟐 − 𝟓𝟎𝒚 = −𝟐𝟓 a. Write this equation in standard form. b. Find the the center of the ellipse. c. Find the foci of the ellipse. d. Find the vertices of the ellipse. e. Sketch the graph of the ellipse below, making sure to include its center, foci, and vertices. The Hyperbola 6. Consider the following hyperbola below. (𝒙 + 𝟑) 𝟐 𝟏𝟔 − (𝒚 + 𝟐) 𝟐 𝟐𝟓 = 𝟏 a. Find the center of the hyperbola. b. Find the foci of the hyperbola. c. Find the vertices of the hyperbola. d. Find the asymptotes of the hyperbola. e. Sketch the graph the hyperbola below, making sure to include its center, foci, vertices, and asymptotes.