Dba for pre-!
whats are some super useful things i should know about parabolas, ellipses, hyperbolas, parametric equations and polar coordinates? my teacher wants me to explain 3 topics to her tomorrow (7-20-19). i know that i should know this but i've been studying for over an hour and i still don't understand the module. give me an actual answer, i will report if it's not useful to me.

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.

y = - 6

step-by-step explanation:

given the point (- 2, y) lies on the graph then it is a solution of it's equation.

substitute x = - 2 into the equation for value of y

y = 3(- 2) = 3 × - 2 = - 6

the point on the graph is (- 2, 6)

594 square inches

step-by-step explanation:

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