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Answer:
Step-by-step explanation:
Here are some facts you can mention:
1. Parabola.
The equation of a parabola is one where x^2 is the term of the highest degree. ( the degree being '2' in x^2). For example y = x^2, y = 2x^2 - 5x,
y = -x^2 + 1 are all parabolas. Also we have the type x = f(y) - for example
4x = y^2.
The graph looks like a U ( which maybe on its side or upside down The graph of a parabola where the term coefficient of x^2 is positive opens upwards while if it is negative it open downwards.
It is also a 'conic section' . A parabola is formed when we intersect a right cone with a plane surface through the side wall and through the base.
When a projectile is fired from a gun at an angle, the path it follows is close to a parabola. If fired in a vacuum the path we would be exactly parabolic.
2. Ellipse.
This is another conic section formed when we intersect the cone with a plane surface at an angle to the base ( not 90 degrees) and the plane passes through both sides walls of the cone.
It is oval shaped. The path of the planets around our sun form an ellipse.
You can draw an ellipse by fixing 2 pins at a distance apart on a sheet of paper, and tie the ends of a piece of string, longer in length than the distance between the pins, to each pin. We then press a pen or pencil to the string at some point and draw around the 2 pins.
3. Parametric equations.
A third variable is introduced in a parametric equation. Both x and y are written in terms of this third variable. This variable is called a parameter , hence the name parametric equation.
Many functions can be written in the form y = f(x) or x = f(y) but there are some that cannot be written this way. An example is the circle
x^2 + y^2 = r^2. There are many other such functions. By introducing another variable we are able to identify any point on the graph and it also makes the calculus work easier.
The variable used is usually t or the Greek letter theta (for angles). An example of parametric equations are the ones for a parabola: x= at^2, y = 2at,
which are the parametric equation for the parabola y^2 = 4ax.
I hope this helps.
Answer:
Step-by-step explanation:
I have the same problem. Do you still have the answers. I know I'm two years late but just checking.
