Ok so this week we dont have a teacher again so theres stuff i need help on. Anyway i really understand and remember trig stuff and trig functions. I understand the 6 trig functions and how to use them.
The trig functions are:
sin 0= y/r
cos 0= x/r
tan 0= y/x
csc 0= r/y
sec 0= r/x
cot 0= x/y
Waht i need help on is the formulas for hyperbolas and circles and stuff like that and i needa know what i need to find for each
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Circles:
ReplyDeleteThe 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
Alrighty well ill try to help you out a bit...
ReplyDeleteHyperbolas:
Standard Form:
((x-h)^2/a^2)-((y-k)^2/b^2)= 1
The a^2 is always the value under the positive term in the equation.
Circles:
Standard Form: (x-h)^2+(y-k)^2= r^2
Center: (h,k)
The value for r is the radius!!!
Hope this helped :)
Hyperbolas:
ReplyDeleteFor hyperbolas, the formula is (x-h)^2/(length/20^2)-(y-k)^2/(length/2)^2 =1 or -(x-h)^2/(length/2)^2+(y-k)^2/(length/2)^2 =1....i know thats a little confusing. So after u put it in that form, then you will follow steps in order to make a graph:
1. Center (h,k)
2. Major axis is non-negative
3. vertex +/- the square root of the non-negative denominator
4. asymptotes: y+/- sqr. root of y denom/sqr. root of x denom
5. focus^2=x denom + y denom
focus^2=vertex^2+other denom
6. then to sketch the graph make sure u have:
-shape
-center
-major axis
-minor axis
-other interger...if any
-focus
-asymptotes
-vertex
To sketch:
1. Draw a box using the vertex and sqr. root of other denom.
2. Draw diagonals through the box
3. Sketch parabola on each vertex
4. Label foci and asymptotes