So I've completely forgotten everything about conic sections since this last summer where I took Calc 1. This seems pretty easy and whatnot but here's the questions:
(x+3)^2/25 + y^2/12=1
Find:
Center
Major Axis
Vertices
Co-Verticies
Foci
Please have detail
(x+3)^2/25 + y^2/12=1
Find:
Center
Major Axis
Vertices
Co-Verticies
Foci
Please have detail
-
you remember that the form of an ellipse is (x^2)/a^2 + (y^2)/b^2=1
so your a=5 and b=sqrt12
center point would normally be 0,0 BUT it has been shifed because its not just x^2 its (x+3)^2 same for y.
so its like inserting another number within x so when you calculate it your skipping to x+3. understand? so if you skip to a higher number you essentially just move it left. opposite for if you skip to a lower number.
so our center is (0-3),(0+0) = -3,0
major axis is the longest line right through the ellipse. so in this case major axis is the x axis because 5>sqrt12
its equal to 2*a, a=5 therefore the axis is 10.
verts is when y=0 if the y is not shifted.
(x+3^2)/25 + (0^2)/12=1
(x+3^2)/25 =1
x+3=sqrt25 (remember -1*-1=1 and 1*1=1)
x=+-5 -3 so, x=5-3=2, and x=-5-3=-8
co verticies is when x=0 if the x is not shifted. but it is.
the highest and lowest points will be the same if x is shifed
so we can ignore the 3 leaving (y^2)/12=1
y=+-sqrt12
foci are fun points.
http://cadsetterout.com/wp-content/uploads/2010/11/image42_thumb.png
so foci of unshifted is
c^2=a^2-b^2
c=+-sqrt(25+12)=+-sqrt37
but it is shifted 3 to the left.
so we just minus 3 from both sides, therefore
foci 1 = -sqrt37 - 3, foci 2=sqrt37 - 3
so your a=5 and b=sqrt12
center point would normally be 0,0 BUT it has been shifed because its not just x^2 its (x+3)^2 same for y.
so its like inserting another number within x so when you calculate it your skipping to x+3. understand? so if you skip to a higher number you essentially just move it left. opposite for if you skip to a lower number.
so our center is (0-3),(0+0) = -3,0
major axis is the longest line right through the ellipse. so in this case major axis is the x axis because 5>sqrt12
its equal to 2*a, a=5 therefore the axis is 10.
verts is when y=0 if the y is not shifted.
(x+3^2)/25 + (0^2)/12=1
(x+3^2)/25 =1
x+3=sqrt25 (remember -1*-1=1 and 1*1=1)
x=+-5 -3 so, x=5-3=2, and x=-5-3=-8
co verticies is when x=0 if the x is not shifted. but it is.
the highest and lowest points will be the same if x is shifed
so we can ignore the 3 leaving (y^2)/12=1
y=+-sqrt12
foci are fun points.
http://cadsetterout.com/wp-content/uploads/2010/11/image42_thumb.png
so foci of unshifted is
c^2=a^2-b^2
c=+-sqrt(25+12)=+-sqrt37
but it is shifted 3 to the left.
so we just minus 3 from both sides, therefore
foci 1 = -sqrt37 - 3, foci 2=sqrt37 - 3