Mathematics 30 — Conics Homework I
A
Name:
Section 1. Work must be neat and orderly.
1. How must a cutting plane intersect a double-napped cone to produce a circle?
2. The angle between the generator and the axis of a double-napped cone is 32◦ . What
conic is produced if a cutting plane intersects the cone at 30◦ ?
3. What is the intersection of a double-napped cone and a cutting plane perpendicular
to the axis, and passing through the vertex?
4. Sketch the graph of x2 + y 2 = 1, after it has been stretched horizontally by a factor
of 2, and vertically by a factor of 3.
3
2
1
−3
−2
−1
−1
1
2
3
−2
−3
5. What is the equation of the circle with center (2, −3) and radius 5?
1
6. What is the equation of the circle that is tangent to the x axis at 7, and the y axis at
7?
7. What change must be made the equation x2 + y 2 = 36 in order to stretch the circle
vertically by a factor of 3?
8. Write the following circle in general form: (x − 1)2 + (y + 2)2 = 9.
9. Write the following circle equation in standard form: x2 + y 2 − 6x − 8y + 21 = 0.
10. Write the following ellipse in general form:
x2 y 2
+ 2 =1
22
3
11. Write the following ellipse equation in standard form: 9x2 + 4y 2 + 18x − 8y − 23 = 0
2
Mathematics 30 — Conics Homework I
B
Name:
Section 1. Work must be neat and orderly.
1. How must a cutting plane intersect a double-napped cone to produce a parabola?
2. The angle between the generator and the axis of a double-napped cone is 32◦ . What
conic is produced if a cutting plane intersects the cone at 32◦ ?
3. What is the intersection of a double-napped cone and a cutting plane parallel to the
generator,and passing through the vertex?
4. Sketch the graph of x2 + y 2 = 1, after it has been stretched horizontally by a factor
of 3, and vertically by a factor of 2.
3
2
1
−3
−2
−1
−1
1
2
3
−2
−3
5. What is the equation of the circle with center (−4, 1) and radius 3?
1
6. What is the equation of the circle that is tangent to the x axis at −7, and the y axis
at 7?
7. What change must be made the equation x2 + y 2 = 36 in order to stretch the circle
horizontally by a factor of 3?
8. Write the following circle in general form: (x − 1)2 + (y − 2)2 = 9.
9. Write the following circle equation in standard form: x2 + y 2 + 6x − 8y + 21 = 0.
10. Write the following ellipse in general form:
x2 y 2
+ 2 =1
32
5
11. Write the following ellipse equation in standard form: 9x2 + 4y 2 − 18x + 8y − 23 = 0
2
Mathematics 30 — Conics Homework I
C
Name:
Section 1. Work must be neat and orderly.
1. How must a cutting plane intersect a double-napped cone to produce a ellipse?
2. The angle between the generator and the axis of a double-napped cone is 32◦ . What
conic is produced if a cutting plane intersects the cone at 34◦ ?
3. What is the intersection of a double-napped cone and a cutting plane parallel to the
axes,and passing through the vertex?
4. Sketch the graph of x2 + y 2 = 1, after it has been stretched horizontally by a factor
of 2, and vertically by a factor of .5.
3
2
1
−3
−2
−1
−1
1
2
3
−2
−3
5. What is the equation of the circle with center (6, −2) and radius 7?
1
6. What is the equation of the circle that is tangent to the x axis at −7, and the y axis
at −7?
7. What change must be made the equation x2 + y 2 = 36 in order to stretch the circle
vertically by a factor of 2?
8. Write the following circle in general form: (x + 1)2 + (y + 1)2 = 9.
9. Write the following circle equation in standard form: x2 + y 2 − 6x + 8y + 21 = 0.
10. Write the following ellipse in general form:
x2 y 2
+ 2 =1
52
2
11. Write the following ellipse equation in standard form: 9x2 + 4y 2 + 18x + 8y − 23 = 0
2