Parabola Parts Equation of Ellipse 1 Parabola UpDown

Parabola Parts Equation of Ellipse (1) Parabola (UpDown) Equation of Ellipse (2) Parabola (LeftRight) Hyperbola (Left Right) Equation of Parabola (Vertex, Focus) Hyperbola (Up Down) Equation of Parabola (Vert, Direct) Equation of Hyperbola (1) Equation (Line tangent to circle at a point) Equation of Hyperbola (2) Ellipse (Tall) Ellipse (Wide) Please report any errors ASAP by email to sakim@fjuhsd. net or IM at kimtroymath. Problems may be more difficult on test. Consult homework assignment. Not all topics covered.

Updown parabola Right (pos)Left(neg) parabola Vertex Focus Directrix Axis of Symmetry How to graph 6) Latus Rectum = 1) Opens |4 p| through 2) Vertex, aos focus 3) Find p 4) Focus 5) Directrix Focus – On a. o. s. , is inside the parabola Directrix – perpendicular to a. o. s, is outside the parabola All points on the parabola are equidistant from the focus and the directrix

How to graph 1) Opens Down 2) Vertexaos (3, 4); x = 3 3) Find p p = -2 4) Focus (3, 4 + (-2)) = (3, 2) 5) Directrix y = 4 – (-2) y = 6 Latus Rectum |4 p| = 8 Don’t have to necessarily memorize, just think about these. x=3 (3, 4) (3, 2)

1) Opens Right 2) Vertex, aos (-5, -2), y = -2 3) Find p 4) Focus 5) Directrix Latus Rectum (-5, -2) |4 p| = 12 Don’t have to necessarily memorize, just think about these. y = -2

Equation of parabola given vertex and focus. Vertex (2, 1) Focus (4, 1) 1) Opening 2) Vertex 3) Find p 4) Plug in parts

Equation of parabola given vertex and directrix. Vertex (2, -3) Directrix y = 1) Opening 2) Vertex 3) Find p 4) Plug in parts

Equation of tangent line given center, point 1) Find center (3, -1) 2) Other point (5, 3) 3) 2) Find slope 4) 3) Perp Slope 5) 4) Eq of line (x - 3)2 + (y + 1)2 = 20 (5, 3) is point on circle

1) Tall or Wide? 2) Find center 3) Find a and plot 4) Find b and plot 5) Find c and plot

NOTE: If you have a and b, you don’t need c Vertices: (4, 0), (-2, 0) 1 – Find Center 2 – Tall or Wide 3 – Find a: b: c: 4 – Find what you don’t have 5 – Plug it in Foci: (2, 0), (0, 0)

NOTE: If you have a and b, you don’t need c Co-Vertices: (5, -1), (-3, -1) 1 – Find Center 2 – Tall or Wide 3 – Find a: b: c: 4 – Find what you don’t have 5 – Plug it in Foci: (1, 8), (1, -10)

Steps 1 – Find Center 2 – Find a and plot 3 – Find b and plot 4 – Make box and sketch asymptotes 5 – Find c, foci 6 – Sketch 7 – Equation of asymptotes

Vertices: (4, 0), (-2, 0) 1 – Find Center 2 – UpDown, or LeftRight 3 – Find a: b: c: 4 – Find what you don’t have 5 – Plug it in Foci: (5, 0), (-3, 0)

Vertices: (1, -3), (1, 5) 1 – Find Center 2 – UpDown, or LeftRight 3 – Find a: b: c: 4 – Find what you don’t have 5 – Plug it in Foci: (1, -5), (1, 7)