Exam 7: Conic Sections

Find the standard form of the equation of the ellipse satisfying the given conditions. -Endpoints of major axis: (-10, -4)and (6, -4); endpoints of minor axis: (-2, -8)and (-2, 0)

Find the standard form of the equation of the hyperbola. -

Use the center, vertices, and asymptotes to graph the hyperbola. - $(y+4)^{2}-4(x+3)^{2}=4$

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - $4 x ^ { 2 } - 16 y ^ { 2 } - 16 x - 32 y - 64 = 0$

Graph Ellipses Not Centered at the Origin - $4 ( x - 1 ) ^ { 2 } + 16 ( y - 2 ) ^ { 2 } = 64$

Graph Hyperbolas Not Centered at the Origin Find the location of the center, vertices, and foci for the hyperbola described by the equation. - $\frac { ( x - 1 ) ^ { 2 } } { 49 } - \frac { ( y + 4 ) ^ { 2 } } { 36 } = 1$

Additional Concepts Determine the direction in which the parabola opens, and the vertex. - $y = x ^ { 2 } - 6 x + 5$

Write Equations of Ellipses in Standard Form -

Find the vertices and locate the foci for the hyperbola whose equation is given. - $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 121 } = 1$

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. - $y = x ^ { 2 } + 2 x - 4$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$

Graph Parabolas with Vertices Not at the Origin Find the vertex, focus, and directrix of the parabola with the given equation. - $( y + 2 ) ^ { 2 } = 20 ( x + 3 )$

Write Equations of Parabolas in Standard Form Find the standard form of the equation of the parabola using the information given. -Focus: $( - 7,3 )$ ; Directrix: $x = 3$

Graph Parabolas with Vertices Not at the Origin Find the vertex, focus, and directrix of the parabola with the given equation. - $( x - 1 ) ^ { 2 } = - 7 ( y + 2 )$

Write Equations of Parabolas in Standard Form Find the standard form of the equation of the parabola using the information given. -Focus: $( 2,8 ) ;$ Directrix: $y = 0$

Write Equations of Parabolas in Standard Form Find the standard form of the equation of the parabola using the information given. -Focus: $( 0 , - 15 )$ ; Directrix: $\mathrm { y } = 15$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Foci: $( 0 , - 4 ) , ( 0,4 )$ ; vertices: $( 0 , - 7 ) , ( 0,7 )$

Graph Parabolas with Vertices Not at the Origin Find the vertex, focus, and directrix of the parabola with the given equation. - $( \mathrm { y } - 1 ) ^ { 2 } = 16 \mathrm { x }$

Graph Hyperbolas Centered at the Origin Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes. - $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$

Write Equations of Hyperbolas in Standard Form -Center: $( 6,3 ) ;$ Focus: $( 4,3 ) ;$ Vertex: $( 5,3 )$