Devin's Reflection

Ch. 6 Conics

The standard equation of a circle is (x-h)^2+(y-k)^2 .....the center is (h,k)

To find the intersection of a line and a circle:

1. solve the linear eqn for y.
2. substitute in the circle eqn.
3. solve for x.
4. plug the x value in to get the y value.

If your x value is imaginary, then there is no point of intersection.

EX: find the center and radius.(x-3)^2+(y+7)^2=19

c:(h,k)

center: (3,-7)

radius: square root of 19

--Parabolas have no major axis and no asymptotes.

Axis of symmetry x=-b/2a

Finding the vertex
(-b/2a, f(-b/2a))

or

complete the square to get vertex form
y=(x+a)^2+b a&b are #'s

(-a,b) vertex

focus: 1/4p= coeff of x^2 then add p.

directrix is p units behind vertex. subtract p.

EX: 1/8y^2

v(0,0)

Focus: p=2(2,0)

directrix: x=-2