Pre-Calculus
REVIEW: Conics Days 1 & 2 (Parabolas and Ellipses)
Name: _____________________________________
1. Which of the following is the standard form of:
5x2 + 2y2 + 30x – 16y + 27 = 0?
a)
c)
e)
( x − 3)
2
+
25
( x + 3)
2
+
10
( x + 3)
10
2
−
( y − 4)
2
=
1
10
( y − 4)
2
=
1
25
( y − 4)
b)
d)
( x + 3)
2
+
10
( x + 3)
25
2
+
( y + 4)
2
=
1
25
( y − 4)
10
2
=
1
2
25
=
1
2. Identify the conic in question number 1. (Is it a parabola or ellipse?)
3. Graph the ellipse given by
( x − 9)
9
2
+
( y + 3)
36
2
=
1.
For numbers 4 – 7, use the following equation: 2y2 – 16y – 20x + 72 = 0.
4. Identify the vertex.
5. Identify the focus.
6. Identify the axis of symmetry.
7. Identify the directrix.
8. What is the equation for an ellipse with vertices (–7, –3), (13, –3) and foci (–5, –3), (11, –3)?
9. Write an equation for the parabola with vertex (7, 10) and directrix x = 1.
10. What is the eccentricity of the ellipse given by
( x + 9)
10
2
+
( y + 11)
8
2
1? Round to the nearest hundredth.
=
For 11 and 12, determine the orientation of the parabola. (opens up/left/down/right)
11. vertex: (–5, 1), focus (–5, 3)
12. directrix: y = 4; p = –2
13. Write the equation for the graph of a parabola with vertex (8, 19) and focus (4.75, 19).
14. Write the equation in standard form of the parabola: y = x2 + 14x – 104.
15. Graph the parabola given by (x – 2)2 = –12(y – 3).
16. Write an equation, in standard form, for the ellipse with the given characteristics: foci (–6, 9), (–6, –3); length of major axis is 20.
17. Write an equation, in standard form, for the ellipse with the given characteristics: vertices: (–10, 0), (10, 0); eccentricity, e, is 0.6.