Analytic Geometry

Group Members Include:Taylor, Suzanne, Analynn and Kerry

The Areas of Analytic Geometry Equation of a CircleCoordinatesSolving Equations AlgebraicallyDistance and Angles

Equation of a Circle

A circle is the set of all points (x,y) that are an equal distance from a point which is called the centre of the circle.

 

The Distance r:

Is the distance between the centre of

the circle and

one of the points (x or y) is called the radius.

r2 = x2 + y2

This formula is used when the centre of the circle is located at the origin (the origin is the coordinates 0,0) (5, 3)

r2 = 52 + 32

r2 = 25 + 9

r2 = 34

r =

 If the centre is located at

some point (h,k) then the distance from the point (h,k) to any point P (x,y) on the circle is:

r2=(x-h)2 +(y-k)2

(x +1) 2+ (y-2) 2 = 20

The equation can come in two different forms.

The one above or x2 +y2 +dx +ey +f = 0 if it comes in this form we can convert it to the first form by completing the square.

4x2 + 4y2 + 20x - 16y + 37 = 0

4x2 + 4y2 + 20x - 16y + 37 = 0 General form

x2 + y2 + 5x - 4y = 0 Divide by 4.

Group terms.

Complete the square by adding and 4 to both sides.

= 1 Standard form

How To GraphBy: Taylor Gouzecky

Solving linear equations by graphing is simple, here are steps to help you through the equation y=2x+3.

First draw a t-chart.

The left column contains x-values and the right has y-values.

Pick some values for x, it’s good to pick at least three.

Once you choose the x-values, add them into the equation figuring out the y-values.

Now that you have your x and y values, put them into a graph.

Now plot your points.

Connect the dots.

The questions get harder, you may get one like :

4x-3y=12Find out what y is:

So your actually graphing

Make a t-chart.

Put the points in and draw the graph