Conic section(Basic)

Analytic geometry

By Wren

Standard form of equations​

Slope intercept form:

y = mx+b​

​

Standard form:

​y-mx-b = 0

mx+b-y = 0​

This is some hard algebra :P​

Distance between point and line​

​​Midpoint = ((x1+x2)/2​, (y1+y2)/2)

Distance x = ​x2-x1

Distance y = y2-y1

Distance :​

​

​

Distance between two points​

​Distances and midpoints

What is this shit?​

Multiple Choice

Midpoint of (5,2) and (9,2)

• (7,2)

• (3,2)

• (2,7)

• (2,3)

Multiple Choice

Midpoint of (-3,3) and (6,9)

• (-1.5,-6)

• (1.5,6)

• (6,1.5)

• (-6,-1.5)

Conic section

By Wren

Formula

Radius​ = r

Center = (h, k)

Tangent(เส้นตัดวงกลม) = Linear functions​

​Structures

C​ircles

Easiest of the bunch, math teacher makes it look hard.​

Multiple Choice

Which equation is the standard equation of a circle?

• $$x^2+y=9$$  

• $$\left(x-1\right)^2+x^2=4$$  

• $$x^2+\left(y-1\right)^2=1$$  

• $$\left(x-1\right)^2-\left(y-1\right)^2=16$$  

Multiple Choice

What is the equation of this circle?

• $$\left(x-1\right)^2+\left(y-1\right)^2=1$$   

• $$\left(x+1\right)^2+y^2=4$$  

• $$x^2+y^2=16$$  

• $$\left(x+3\right)^2+y^2=25$$  

Multiple Choice

Circle with center at (0,0) and radius of 7

• $$\left(x+1\right)^2+\left(y-2\right)^2=36$$  

• $$\left(x-2\right)^2+\left(y+1\right)^2=25$$  

• $$x^2+y^2=6$$  

• $$x^2+y^2=49$$  

Multiple Choice

Circle with center at (3,5) and radius of 4

• $$\left(x-3\right)^2-\left(y-5\right)^2=16$$  

• $$\left(x+3\right)^2+\left(y+5\right)^2=16$$  

• $$\left(x+3\right)^2-\left(y+5\right)^2=16$$  

• $$\left(x-3\right)^2+\left(x-5\right)^2=16$$  

Tangent line: ax+by+c = 0

Center = (h1,k1)​

Radius:​

Radius formula from tangent:

Point on circle(จุดบนวงกลม) = (h2,k2)

Center = (h2,k1)

Radius:

​

​

Radius formula from points on circle:​

Radius and Tangent lin​e

Circle on crack I guess :P​

Multiple Choice

A circle with a center at (6,9) with a point on the circle at (1,-3)

• $$\left(x-9\right)^2+\left(y-6\right)^2=144$$  

• $$\left(x-6\right)^2+\left(y-9\right)^2=169$$  

• $$\left(x-9\right)^2+\left(y-6\right)^2=169$$  

• $$\left(x-6\right)^2+\left(y-9\right)^2=144$$  

Multiple Choice

A circle with a center at (1,-1) and a tangent line function of 9x+12y+18=0. Which is the equation of this circle?

• $$\left(x-1\right)^2+\left(y+1\right)^2=9$$  

• $$\left(x+1\right)^2+\left(y-1\right)^2=1$$  

• $$\left(x-1\right)^2+\left(y+1\right)^2=1$$  

• $$\left(x+1\right)^2+\left(y-1\right)^2=9$$  

Formulae​:

Major axis(แกนเอก) = a

Minor axis(แกนโท) = b

Center = (h,k)

Focus length = ​c

Structure​s:

Ellipses​

Circle with extra steps, significantly harder but still understandable.

a is on the y-axis

b is on the x-axis​

Vertical:​

a is on the x-axis

b is on the y-axis​

​Horizontal:

Direction of ellipses

Two!? I thought one was already bad enough!​

Multiple Choice

Which is the standard equation for an ellipse?

• $$\frac{\left(x+h\right)^2}{a^2}+\frac{\left(y+k\right)^2}{b^2}=1$$  

• $$\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=r^2$$  

• $$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$$  

• $$\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1$$  

Multiple Choice

$$\frac{x^2}{36}+\frac{y^2}{16}=1$$  

Which direction will the ellipse stretch in?

• Horizontally

  (แนวนอน)

• Vertically

  (แนวตั้ง)

Multiple Choice

$$\frac{x^2}{64}+\frac{y^2}{100}=1$$  

Which direction will the ellipse stretch in?

• Horizontally

  (แนวนอน)

• Vertically

  (แนวตั้ง)

Multiple Choice

$$\frac{\left(x-2\right)^2}{36}+\frac{\left(y+9\right)^2}{169}=1$$  

Which direction will the ellipse stretch in?

• Horizontally

  (แนวนอน)

• Vertically

  (แนวตั้ง)

​Focus point is always on the a-axis

c = focus length

a = major axis(​แกนเอก)

b = minor axis(​แกนโท)

Focus length formula:​

Focus point

I thought it was only center and radius and we have this ;-;​

Multiple Choice

$$\frac{\left(x+2\right)^2}{9}+\frac{\left(y-1\right)^2}{4}=1$$  

Which axis is the focus length on?

• x-axis

• y-axis

Multiple Choice

$$\frac{\left(x+2\right)^2}{25}+\frac{\left(y-1\right)^2}{49}=1$$  

Which axis is the focus length on?

• x-axis

• y-axis

​Eccentricity formula:

Latus rectum formula:​

Latus rectum and Eccentricity

If I were to choose between this and sh​itting my pants I wouldn't need a toilet.

​a = major axis(​แกนเอก)

b = minor axis(​แกนโท)

​a = major axis(​แกนเอก)

​c = focus length

​End of

​Basic Conic section