9-6 Identifying Conic Sections
Write each equation in standard form. State whether the graph of the equation is a parabola, circle,
ellipse, or hyperbola. Then graph the equation.
15. SOLUTION: The given equation is an ellipse.
Graph the function.
17. SOLUTION: The given equation is a parabola.
Graph the function.
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9-6 Identifying Conic Sections
17. SOLUTION: The given equation is a parabola.
Graph the function.
19. SOLUTION: The given equation is a circle.
Graph the function.
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SOLUTION: Page 2
9-6 Identifying Conic Sections
21. SOLUTION: The given equation is a hyperbola.
Graph the function.
23. SOLUTION: The given equation is a hyperbola.
Graph the function.
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9-6 Identifying Conic Sections
23. SOLUTION: The given equation is a hyperbola.
Graph the function.
Without writing in standard form, state whether the graph of the equation is a parabola, circle, ellipse, or
hyperbola.
25. SOLUTION: A = 4, B = 0, and C = 4
The discriminant is
.
Because the discriminant is less than 0, B = 0 and A = C, the conic is a circle.
27. SOLUTION: A = 18, B = 0, and C = 4
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The discriminant is
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.
A = 4, B = 0, and C = 4
The discriminant is
.
9-6 Identifying
Sections
Because the Conic
discriminant
is less than 0, B = 0 and A = C, the conic is a circle.
27. SOLUTION: A = 18, B = 0, and C = 4
The discriminant is
.
Because the discriminant is less than 0 and B = 0, the conic is an ellipse.
29. SOLUTION: A = 12, B = 5, and C = –3
The discriminant is
.
Because the discriminant is greater than 0, the conic is a hyperbola.
31. SOLUTION: A = 8, B = 20, and C = –4
The discriminant is
.
Because the discriminant is greater than 0, the conic is a hyperbola.
33. SOLUTION: A = –27, B = 324, and C = –3
The discriminant is
.
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Because the discriminant is greater than 0, the conic is a hyperbola.
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The discriminant is
.
9-6 Identifying
Conic Sections
Because the discriminant is greater than 0, the conic is a hyperbola.
33. SOLUTION: A = –27, B = 324, and C = –3
The discriminant is
.
Because the discriminant is greater than 0, the conic is a hyperbola.
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