Conic Sections — Drills
Conic Sections has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 6 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Coefficient — The number multiplying a variable — the 3 in 3n.
- Open — Open excludes the endpoint (<, >); closed includes it (≤, ≥).
- Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
- Radius — Centre to edge. Half the diameter.
- Parabola — The U-shaped graph of a quadratic function.
- Vertex — A turning point of the curve, on its axis.
Identifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What curve is x29 - y24 = 1?
- A circle
- An ellipse
- A parabola
- A hyperbola
Worked answer
A hyperbola
Two squares with opposite signs
Problem 2
What curve is x225+y216=1?
- A circle
- An ellipse
- A parabola
- A hyperbola
Worked answer
An ellipse
Two squares, same sign, different coefficients
Circle
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For (x+5)2+(y-2)2=36, give the centre as an ordered pair.
Worked answer
(-5,2)
(x+5) gives -5 and (y-2) gives 2
Problem 2
For (x+1)2+(y-0)2=4, give the radius.
Worked answer
2
√4 = 2
Ellipse
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For x264+y236=1, how far does the curve reach along the x-axis?
Worked answer
8
√64 = 8
Problem 2
For x24+y225=1, how far does the curve reach along the y-axis?
Worked answer
5
√25 = 5
Hyperbola
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which way does y225-x29=1 open?
- Left and right
- Up and down
- All four ways
- It does not open
Worked answer
Up and down
The y2 term is the positive one
So it opens up and down
Problem 2
Which way does x216-y216=1 open?
- Left and right
- Up and down
- All four ways
- It does not open
Worked answer
Left and right
The x2 term is the positive one
So it opens left and right
Completing
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For x2+y2-8x+8y - 17 = 0, find the radius.
Worked answer
7
(x-4)2+(y+4)2 = 49
r = 7
Problem 2
For x2+y2-12x+6y + 29 = 0, find the radius.
Worked answer
4
(x-6)2+(y+3)2 = 16
r = 4