Exam 60: Introduction to Conics Parabolas

Find the center and vertices of the hyperbola and sketch its graph,using asymptotes as sketching aids.​ $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ ​

Find the equation of the parabola so that its graph matches the description.​ $( y + 2 ) ^ { 2 } = 3 ( x - 7 )$ ;lower half of parabola ​

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure).Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin. )​ $a = 4.5$ ​

Find the equation of the parabola so that its graph matches the description.​ $( y - 5 ) ^ { 2 } = 2 ( x + 1 )$ ;upper half of parabola ​

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. ​ Parabola: $x ^ { 2 } + 20 y = 0$ Tangent Line: $x + y - 5 = 0$ ​

Find the vertex and focus of the parabola from the given equation and select its graph.​ $y = \frac { 1 } { 6 } x ^ { 2 }$ ​

Find the vertex,focus,and directrix of the parabola.​ $y ^ { 2 } = 10 x$ ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( - 3,0 )$

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Find the vertex,focus,and directrix of the parabola.​ $y = - 3 x ^ { 2 }$ ​

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7,-2)focus: (-5,-2)

Select the graph of the following equation: ​​ $y ^ { 2 } = - 2 x$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Horizontal axis and passes through the point $( 3 , - 2 )$ ​

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7,-9)directrix: $x = - 9$

Give the coordinates of the circle's center and its radius.​ $x ^ { 2 } + y ^ { 2 } - 64 = 0$ ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Focies: (±7,0);major axis of length 16 ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Horizontal axis and passes through the point $( - 4,7 )$ ​

Find the standard form of the equation of the hyperbola with the given characteristics. focies: (±4,0),asymptotes: $y = \pm 5 x$

Find the vertex and directrix of the parabola. $x ^ { 2 } - 18 x - 12 y + 33 = 0$

Find the vertex,focus,and directrix of the parabola.​ $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$ ​