Pure Math 30
Conics Review
1. The conic section formed when a plane intersects a right circular
double napped cone parallel to the axis could be a _________ or
_______
2. If the plane intersects the axis at an angle of 48 and the vertex
angle is 80 then the conic section formed is __________
3. The graph of the relation 5x2 – 3y2 + 4x – 3y + 12 = 0 is _______
( x  4)2 y 2
4. The graph of the relation

 1 is ________
9
9
5. Given the relation x – 4 = 2(y + 3)2, then
a) the domain is _____
b) the range is _____
c) the vertex is _____
d) the x-intercept is _____
( x  2)2 ( y  3) 2

 1 is transformed to
6. When the graph of the relation
4
9
( x  2)2 ( y  1) 2

 1 , then the transformations which have taken place
16
9
are _______
7. Given the graph of a circle with diameter joining the points (5,1) to
(-3,7), the equation of this relation is _____
( x  1)2 ( y  2)2

 1 is stretched vertically
8. The hyperbola defined by
9
4
by a factor of 2 and is translated 3 units up and 1 unit to the left. The
new relation is __________
9. The relation y – 3 = 4(x + 1)2 written in general form is _______
10. The relation 4x2 + 5y2 – 16x + 30y + 41 = 0 written in standard form is
_________
11. The equation of the ellipse formed with vertices at (-2, 1) and (6, 1)
that passes through the point (2, 3) is __________
12. A circle with centre at (5, -2) and radius 3, is stretched vertically
about the centre by a factor of 4, reflected in the y-axis and then
translated 4 units down. The equation of the new quadratic relation is
_________
13. A tunnel is in the shape of a “semi-ellipse”. The width of the tunnel at
the bottom is 3 m, while the height of the tunnel in the middle is 2 m.
If objects which are 2.5 m wide are dragged through the tunnel, then
the maximum height, to the nearest tenth of a metre, the object may
be is _____________
Answers:
1. hyperbola; two intersecting lines 2. ellipse 3. hyperbola
4. circle 5a) x4 b) yR c) (4,-3) d) 22
6. stretched horizontally about the centre by a factor of 2 and
translated down 4 units 7. (x-1)2+(y-4)2=25 8.
( x  2)
2

9
2
9. 4x +8x-y+7=0 10.
12.
( x  5)
9
2

( y  6)
144
2
1
( x  2)
2

( y  3)
5
13. 1.1 m
4
2
1
11.
( x  2)
16
2

( y  7)
16
( y  1)
4
2
1
2
 1