Alicia's Reflection #6

Alrighty so this week we learned a good bit of information: circles, ellipses, and hyperbolas.

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

If the equation is not in standard form, you must complete the square to put it in standard form.

If you are given a center and a point, you can use the distance formula to find the radius.

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.

***Reminder. 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

EX: find the eqn of the circle with the center (1,4) through (3,7)

in the problem you are given a center and a point so you would plug into the distance formula.

square root of (3-1)^2+(7-4)^2= square root of 4+9=square root of 13. **13 has no root.

Your answer should be (x-1)^2+(y-4)^2=13