14.1. Conic Sections
Conic sections include circles, hyperbolas, parabolas and ellipses with equations:
Circle: x2 + y2 = r2 and (x – h)2 + (y – k)2 = r2
Parabola: y = a(x –h)2 + k and x = a(y –h)2 + k
Hyperbola: x2/a2 – y2/b2 = 1
Ellipse: x2/b2 + y2/a2 = 1
Parabola: y = a(x –h)2 + k and x = a(y –h)2 + k
Hyperbola: x2/a2 – y2/b2 = 1
Ellipse: x2/b2 + y2/a2 = 1
Type the equation as given in the problem with one equation per line. Hit enter after each equation.
Examples
Sketch the graph of each conic section.
Examples
Sketch the graph of each conic section.
1. x2/4 – y2/9 = 1 (hyperbola)
2. y = 2x2 –1 (parabola)
3. y = -x2 – 2 (parabola)
4. x2/2 + y2/4 = 1 (ellipse)
5. x2 + y2 = 9 (circle)
2. y = 2x2 –1 (parabola)
3. y = -x2 – 2 (parabola)
4. x2/2 + y2/4 = 1 (ellipse)
5. x2 + y2 = 9 (circle)
Calculator solutions
Enter each of the following. Type y by tapping the x variable twice.
1) x^2/4 - y^2/9 = 1
2) 2x^2 - 1
3) -x^2 - 2
4) x^2/2 + y^2/4 = 1
5) x^2 + y^2 = 9
Enter each of the following. Type y by tapping the x variable twice.
1) x^2/4 - y^2/9 = 1
2) 2x^2 - 1
3) -x^2 - 2
4) x^2/2 + y^2/4 = 1
5) x^2 + y^2 = 9
To look at each graph individually, enter one equation per workspace.
