Ahhhh! CONICS. This week was not that good for me. I do not like conics. I get all the formulas mixed up and it becomes a big jumbled mess. It is mostly ellipses and hyperbolas that I have problems with so I will explain the rules for circles (which I do get) for this reflection.
1. the eqn for a circle in standard form: (x-h)^2+(y-k)^2=r^2 where the center=(h,k) and r=radius
2. if eqn is not already in standard form, you must complete the square to put in standard form
3. given the 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 of the line
2. substitute in circle eqn
3. solve for x
4. plug x value in to get y value
*NOTE: if your x-value is imaginary, then there is no point of intersection
Given the Equation (x-3)^2+(y-7)^2=19 find th ecenter and radius
CENTER: (3,7) RADIUS: ⌋19
B. x^2+y^2+12y+16x-5
x^2+16x+64+y^2+12y+36=5+64+36
(x+8)^2+(y+6^2)=105
Center: (-8,-6) Radius: ⌋105
The main problem I have had with the homework over the weekend is where the point on the minor axis comes from. I don't quite understand it. And also, numbers 19-22 on the homework. If anyone knows how to do this, I would like to know. Thanks.
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