Circles
Parabolas
Lines
Complete the square
Transformations
100
What is the equation for a circle?
(x-h)^2+(y-k)^2=r^2
100
What is the equation for a parabola?
(x-h)^2+(y-k)^2=(y-d)^2
100
What is our equation for a line?
(y-k)=m(x-h)
100
What number do you divide by 2?
Ex:
x^2+6x+"___"=4+"___"
(x+"___")^2="___"
you divide 6 by 2
100
How do you know if a transformation rule is congruent, similar, or neither?
(x,y)
No multiplication or division means Congruent
Mult/Divide by same # is Similar
Not same # is Neither
200
Write the equation for a circle given (2,4) and r=3
(x-2)^2+(y-4)^2=3^2
200
What is the definition of a parabola?
A group of points equally far away from the focus and directrix
200
How do you change the slope
5/3
to find perpendicular slope?
What is the parallel slope?
-3/5
"flip and change the sign"
5/3 " is parallel- same slope"
200
After completing the square, how do you find the center and radius?
(x-h)^2+(y-k)^2=r^2
so (h,k) is the center (change signs)
and its equal to r2, so
sqrt("what it's equal to")" gives the radius"
200
For the following transformation, state whether the transformation is congruent, similar or neither.
(-y,x)
Congruent
(No multiplication or division)
300
Write the equation for a circle given (-4,5) and r=2
(x+4)^2+(y-5)^2=2^2
300
Write the equation for a parabola given focus (4,2) and directrix y=6
(x-4)^2+(y-2)^2=(y-6)^2
300
Write the equation of a line parallel to
y=-3x+7
that goes through (2,4)
(y-4)=-3(x-2)
300
Find the center and radius of the circle
x^2+y^2-8x+2=4y
x^2-8x+"___"+y^2-4y+"___"=-2+"___"+"___"
(x+"___")^2+(y+"___")^2="___"
x^2+y^2-8x+2=4y
x^2-8x+"'16'"+y^2-4y+"'4'"=-2+"'16'"+"'4'"
(x+"'-4'")^2+(y+"'-2'")^2="'18'"
"center "(4,2) " and radius " sqrt(18)
300
For the following transformation, state whether the transformation is congruent, similar or neither.
(-2x,2y)
Similar
(Both multiplied by 2- negatives reflect so they have no effect on congruent vs similar because they don't change the size)
400
Is (1,-3) on the circle
(x-2)^2+(y+4)^2=3^2
No
(-1)^2+(1)^2=2!=9
400
Is (0,2) on the parabola
(x-4)^2+(y-2)^2=(y-6)^2
Ye
(0-4)^2+(2-2)^2=(2-6)^2
(-4)^2+0^2=(-4)^2
16=16
400
Label the equations as Parallel, Perpendicular, or Neither to the equation
y=3/5x-4
"a)" y-5=-3/5x+2
"b)" y+5/3x=7
a) neither
b)perpendicular
400
What is the center and radius of the circle?
x^2+y^2+2x-6y=6
(x+1)^2+(y-3)^2=16
Center (-1,3)
Radius 4
400
Do the transformation (x-5,y+3) on the figure
500
Is (2,-1) on the circle with center (2,-4) and r=3
"Yuh"
(x-2)^2+(y+4)^2=3^2
(2-2)^2+(-1+4)^2=3^2
(0)^2+(3)^2=3^2
9=9
500
Is (-8,0) on the parabola with focus (-3,1) and directrix y=5
Nah
(x+3)^{2}+(y-1)^{2}=(y-5)^{2}
(-8+3)^{2}+(0-1)^{2}=(0-5)^{2}
(-5)^2+(-1)^2=(-5)^2
26!=25
500
Write the equation of a line perpendicular to
y=2/3x-15
that goes through (-1,3)
(y-3)=-3/2(x+1)
500
What is the center and radius of the circle?
x^2-10y-4=-y^2-8x
(x+4)^2+(y-5)^2=45
Center (-4,5)
Radius
sqrt45 " or "6.71
500
Do the transformation (-y,x) on the figure
