Devin's Reflection #7

This week we have dealt with conics, ellipses, and hyperbolas. The standard form for a circle equation is (x-h)^2+(y-k)^@=r^2. The center is (h,k).

Examples: Find the center

a. (x-3)^2+(y+7)^2=19

center (3,-7)

b. x^2+y^2-6x+4y-12=0

x^2-6x+ (9)+y^2+4y+ (4)=12+9+4

(x-3)^2+(y+2)^2=25

center (3,-2)

The r stands for the radius of the circle. When the equation is not in standard equation you have to complete the square to put the equation in standard equation. You can determine the radius of a circle, by using the distance formula and if you are given the center and a point.

Example: Find radius

a.(x-3)^@+(y+7)^2=19

radius square root of (19)




To find the intersection of a line and a cirlce

1. solve the linear equation for y
2. substitute in circle equation
3. solve for x
4. plug x-value into get y-value

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

With ellipses, the main thing to know is the steps. They are:

1. Find center
2. Find major axis - big denom.
3. Find vertex - square root of big denom.
4. Find other intercepts - square root of small denom
5. Find Focus
6. Find length of major axis
7. Find length of minor axis
8. Graph

Just like the ellipses, to sketch the hyperbolas you must follow the steps.
First find:

1. shape
2. center
3. major axis
4. minor axis
5. 0ther int.
6. vertex
7. focus
8. asymptotes
9. then sketch

To sketch a hyperbola,do the following

1. Draw a box using the vertex and square root of the other denom
2. Draw diagonals through box
3. Sketch a parabola on each vertex
4. Label focus and asymptotes