We started our class answering these two questions...
- we can find the vertex which is v(-2,1) just by looking at the equation given.
- Since the squared is from the x-side, the parabola will opens up or down.
- By using 4p from the original formula, we can solve for p and get p=3/4.
- value of 3 in the equation is positive so it opens up
- We just need to add and subtract to get the coordinates of the focus and directrix using the p= 3/4 for the y component. (Take note it's from the vertex)
- Therefore, Focus or F(-2, 1.75), directrix will be y=1/4 and axis of symmetry or a.o.s.=-2
- Find the vertex v(-2,0)
- Since the squared is from the y-side, the parabola will opens left or right.
- By using 4p from the original formula, we can solve for p and get p=-2.
- value of 8 is negative so it opens left
- Add and subtract, this time it is the x-coordinate to get the focus and directrix.
- Therefore, F(-4,0), directrix x=0
After that Mr. K gave us a bond paper with a big circle that is drawn in it. It has a point in the center. We did a paper folding on that and the figure of ellipse came out. We figured out that those measurements above are all the same. Mr. K used his big fat ruler to measure the distance. And as you can see all the answers are 46 mm.
With this, it is also the same as pythagorean theorem but what the difference is we switch a and c. We called it "Pythagorean Property". The formula of Horizontal and Vertical Ellipse is shown above.
We use the formula of the horizontal and vertical ellipse...
This is how the modern technology uses the parabola for good purposes like satellites