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Conics Question 1: (Core Concept Example) For each of the double-napped cones below, is the generator angle, and “x” is the angle formed by the cutting plane
and the cone. Label each diagram according to what conic section is formed, and indicate the value or range of values
for “x”.
Conics Question 2: (Core Concept Example) The vertex angle of a double-napped cone is 80°. The angle between the cutting plane and the central axis is x. Determine the value, or range of values, of x which would generate a) a circle b) a parabola
c) an ellipse
d) a hyperbola
State the degenerate case for all of the primary conic sections...
a) a circle b) a parabola
c) an ellipse d) a hyperbola
Need-To-Know-Concept:
A conic section is formed when a plane intersects a double-napped cone.
We analyze the relationship between the generator angle and the
cutting plane angle.
YOU
Will Not
Get
BORED
With Math
RTD PURE MATH 30
UNIT 2: Conics
Conics Question 3: (Diploma Example)
Conics Question 4: (Diploma Example)
Conics Question 5: (Diploma Example)
Need-To-Know-Concepts:
The standard form equation of a circle is given by: The standard form equation of an ellipse is:
x
y
x
y
General Form is given by 2 2 0Ax Cy Dx Ey F b, where , , , ,A C D E F I
All terms arranged on the Left Side, in order
(𝑥2 term, followed by 𝑦2 term, then 𝑥 term, 𝑦 term, constant term)
2 2 2( ) ( )x h y k r
2 2
2 2
( ) ( )1
x h y k
a b
No fractions for any coefficients (𝐴, 𝐶, 𝐷, 𝐸, 𝐹 ∈ 𝐼)
First term (𝑥2 term) must be positive (𝐴 > 0)
Standard Form Examples
Conics Question 6: (Diploma Example)
Conics Question 7: (Core Concept Example) Given the conic given by the equation 16𝑥2 + 9𝑦2 − 32𝑥 + 36𝑦 − 92 = 0,
determine the standard form equation and sketch. State the domain and range.
x- 6 6
y
- 6
6
Conics Question 8: (Core Concept Example)
Given the circle defined by 2 2 8 6 5 0x y x y state the coordinates of the centre, the domain and range, and the
approximate coordinates of any x-intercepts. (Nearest tenth)
Conics Question 9: (Core Concept Example)
Given the graph of the ellipse on the right, (a) Determine the standard and general
form equation, then (b) Find the approximate y-coordinate when x=7.
x- 4 - 2 2 4 6 8 10
y
- 8
- 6
- 4
- 2
2
4
x- 10 - 5
y
5
10
Conics Question 10: (Diploma Example)
x- 2 2 4 6 8 10
y
- 2
2
4
6
8
10
Need-To-Know-Concepts:
The standard form equation of a hyperbola is given by: The standard form equation of a parabola is:
2 2
2 2
( ) ( )1
x h y k
a b 2( )y k a x h
2( )x h a y k
x
y
x
y
x
y
x
y
General Form is still given by 2 2 0Ax Cy Dx Ey F b, where , , , ,A C D E F I
Standard Form Examples
Conics Question 11: (Diploma Example NUMERICAL RESPONSE)
The standard form equation of a hyperbola is 2 2( 2)
14 9
x y. The total distance between the two vertices is _____
units.
Conics Question 12: (Diploma Example)
Conics Question 13: (Diploma Example)
x- 6 - 4 - 2 2 4 6
y
- 6
- 4
- 2
2
4
6
x- 6 - 4 - 2 2 4 6
y
- 6
- 4
- 2
2
4
6
x- 6 - 4 - 2 2 4 6
y
- 6
- 4
- 2
2
4
6
Conics Question 14: (Diploma Example)
Conics Question 15: (Diploma Example)
Conics Question 16: (Diploma Example Numerical Response)
A parabola with the equation 2 2 4 10 0 y x y has a domain of x p , where p N . The value of “p” is _____.
Conics Question 17: (Diploma Example Numerical Response)
A set of 4 quadratic equations listed below have a sequence of “F” (constant, or last term) values “5813”, from top to
bottom. 2 22 5 2 4 5 0 x y x y
2 2 4 8 0 x x y y 2 2 2 4 1 0 x y x y
2 22 2 4 3 0 x y x y Mary is asked to re-order the equations, from top to bottom, so that they are in the order Circle, Ellipse, Parabola, and
Hyperbola. The resulting sequence of “F” values is: _____.
18.
