Conics
These are the curves obtained by the intersection of a plane and a cone.
Conics or Conic sections
Simplify: -3e2 + 17 – 3s2 + 2s2 – 5s3 + 5
-3e2 – s2 – 5s3 + 22
True or False
Radius is the longest chord in a circle.
False. Diameter is the longest chord.
The circle (x - 4)2 + (y + 6)2 = 36 has a center located at what point?
(4, -6)
What is the length the minor axis of the ellipse (x - 4)^2/36 + (y + 2)^2/16 = 1?
8 units
What conic section is formed when the plane intersects only one cone to form an unbounded curve?
Parabola
Factor completely: 3p2 - 2p - 5
(3p - 5)(p + 1)
A tangent is a line in the plane of a circle that intersects the circle at one point. The point of tangency is located (in, on, at) the circle.
on
Convert (x + 12)2 + (y + 3)2 = 16 into general form.
x2 + y2 + 24x + 6y + 137 = 0
Transform (x - 3)2/25 + (y + 2)2/4 = 1 into general form.
4x2 + 25y2 - 24x + 100y + 36 = 0
Forming conic sections requires intersection of ______
A. a plane and 1 right circular cone.
B. a plane and 1 or 2 stacked right circular cones connected at their apexes.
C. a plane and 2 stacked right circular cones connected at their apexes.
B
Simplify: 32n2/24n
4n/3
How are you going to determine the lenght of a circle whose circle is located at (0, 0) and one point is at (-3, 5)?
use DISTANCE FORMULA!
What is the general equation of a circle whose center is located at (-11, -8) with a radius of 4 units long.
x2 + y2 + 22x + 16y + 169 = 0
Transform 4x2 + y2 +16x - 6y - 39 = 0 into standard form.
(x + 2)2/16 + (y - 3)2/64 = 1
A plane perpendicular to the axis of a single cone intersects it to form which conic section?
Circle
Factor completely: 9k2 + 66k + 21
3(3k + 1)(k + 7)
How long is the radius of a circle whose diamter has endpoint (4, -6) and (-2, 2)?
25 units
Write the standard equation of a circle whose center is located at (-2, 3) and tangent to the line 3x - 4y + 6 = 0
(x + 2)2 + (y - 3)2 = 144/25
Define research gap.
I will tell you whether you are right or not if you convince me with your answer.
All are degenerated cases of conic section EXCEPT ________________.
plane
segment
point
line
segment
Simplify: (v2 - 5v - 14)/(v2 + 4v + 4)
(v - 7)/(v + 2)
4.74
Write the general equation of a circle whose center is at (-5, 3) and one point located at (2, 3).
x2 + y2 +10x - 6y - 15 = 0
How does CFC (chlorofluorocarbon) depletes the ozone layer?
Gaseous CFCs can deplete the ozone layer when they slowly rise into the stratosphere, are broken down by strong ultraviolet radiation, release chlorine atoms, and then react with ozone molecules.