Honors Algebra 2
Name: _______________________
Conics Unit Review!!
Date: ________________ Pd: ____
Write each equation in standard form (or vertex form if it’s a parabola). State whether the graph
of the equation is a parabola, circle, ellipse, or hyperbola. State the center or vertex of the
conic section. If it is an ellipse or hyperbola, state the direction of the major/transverse axis.
1. 4 y 2  25 x 2  100
2. x 2  y 2  2 x  6 y  26  0
3.  x  y 2  12 y  28  0
4. 25 y 2  50 y  4 x 2  75
5. Write the equation in vertex form. State the vertex, focus, and equation of the directrix.
Make sure to show the directrix, focus, and vertex on the graph, as well as at least two other
ordered pairs.
14
x  3 y 2  18 y  15
12
10
8
6
4
2
-8 -6 -4 -2
2
4
6
8 10 12 14
-2
Vertex form: ___________________________
-4
-6
Vertex: __________________
-8
Focus: ___________________
Directrix: _________________ ; LLR: __________
6. Find the equation of the circle given the following information. Then graph the circle. State
the center and the radius of the circle.
14
The endpoints of the diameter at (6, 6) and (10, 12)
12
10
8
6
4
2
Center: __________________
Radius: ___________________
Equation: _____________________________
-8 -6 -4 -2
2
-2
-4
-6
-8
4
6
8 10 12 14
7. Find the coordinates of the center, foci, and the lengths of the major and minor axes for the
ellipse with the given equation. Then graph the ellipse.
 x  4
49
2
 y  3

25
2
1
10
8
6
4
2
Center: __________________
Length of major axis: _______
-10 -8 -6 -4 -2
Length of minor axis: _______
2
4
-2
-4
-6
Foci: _____________________
-8
-10
8. Find the coordinates of the center and vertices for the given equation. Then graph the
hyperbola (draw ALL parts including the rectangle and asymptotes).
16 x 2  4 y 2  64
Center: ______________
Vertices: ________________
Length of Transverse Axis: ______
Length of Conjugate Axis: _______
Foci: ________________________
Equation of the Asymptotes: ____________________________
6
8 10
9.
Write the equation of a circle in standard form with center (1, 0) that contains the
point (–3, 2)
Find an equation for the parabola described. You do not have to graph the parabola – the
graph is to help you sketch and visualize the parabola.
10. Vertex at (–1, –2); focus at (0, –2)
-10 -8
-6
-4
11. Focus at (–3, 4); directrix is y = 2.
10
10
8
8
6
6
4
4
2
2
-2
2
4
6
8
10
-10 -8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8
10
Write an equation in standard form for the ellipse described. You do not have to graph the
ellipse – the graph is to help you sketch and visualize the ellipse.
12. Foci (1, 2) and (–3, 2); vertex (–4, 2).
-10 -8
-6
-4
13. Foci (–3, 5) and (–3, –7); length of major axis is 14.
10
10
8
8
6
6
4
4
2
2
-2
2
4
6
8
10
-10 -8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8
10
Write an equation in standard form for the hyperbola described. You do not have to graph
the hyperbola – the graph is to help you sketch and visualize the hyperbola.
14.
center at (–3, –4); focus at (–3, –8); vertex at (–3, –2)
10
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
Find the vertex form, vertex, focus, directrix, and LLR of the parabola. Graph the
equation.
10
15.
 y  1
2
8
 4  x  2 
6
4
2
Vertex Form:
-10 -8
-6
-4
-2
2
-2
-4
Vertex: _________
-6
-8
Focus: _________
Directrix:_________
LLR: ____________
-10
4
6
8
10
Just enough so you know whether or not you are on the right track!! To see complete solutions,
please go to my website and click on the “KEY Review – Conics Unit” on the course calendar.
y2 x2
1. Hyperbola ~ standard form:
  1 ; transverse axis vertical; center (0, 0)
25 4
2. Circle ~ standard form: ( x  1)2  ( y  3)2  36 ; center (–1, –3); radius: 6
3. Parabola ~ vertex form: x  ( y  6)2  8 ; vertex: (–8, –6)
4. Ellipse ~ standard form:
x 2 ( y  1) 2

 1 ; major axis horizontal; center (0, 1)
25
4
5. Vertex form: x  3  y  3  12 ; vertex: (12, 3); opens to the left
2
6. Circle center: (8, 9); Radius = 13
7. Ellipse center: (–4, –3); major axis length = 14, minor axis length = 10
8. Hyperbola center: (0, 0); Vertices: (2, 0) and (–2, 0)
9.
 x  1
2
 y 2  20
10. x 
1
2
 y  2 1
4
11. y 
1
2
 x  3  3
4
12.
13.
14.
 x  1
2
9
 x  3
2
1
5
2
13
 y  4
4
 y  2

 y  1

2
1
49
2
 x  3

2
12
15. Vertex form: x  
1
1
2
 y  1  2 ; vertex: (2, –1); opens to the left
4