Parabola (Left\Right) Hyperbola (Left Right) Parabola Parts Equation of Ellipse (1) Parabola (Up\Down) Equation of Ellipse (2) Parabola (Left\Right) 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) 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. Ellipse (Wide)

Up\down parabola Right (pos)\Left(neg) parabola Vertex Focus Directrix Axis of Symmetry How to graph 1) Opens 2) Vertex, aos 3) Find p 4) Focus 5) Directrix 6) Latus Rectum = |4p| through focus 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

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

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

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

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

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

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

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

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

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) Foci: (5,0), (-3,0) 1 – Find Center 2 – Up\Down, or Left\Right 3 – Find a: b: c: 4 – Find what you don’t have 5 – Plug it in

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