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. 1. SOLUTION:
The given equation represents an ellipse. Graph the function.
3. SOLUTION:
The given equation is a hyperbola. Graph the function.
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9-6 Identifying Conic Sections
3. SOLUTION:
The given equation is a hyperbola. Graph the function.
Without writing in standard form, state whether the graph of each equation is a parabola, circle, ellipse, or hyperbola. 5. SOLUTION:
A = 4, B = 0, and C = 6
The discriminant is
.
Because the discriminant is less than 0 and A ≠ C, the conic is an ellipse. 7. SOLUTION:
A = 8, B = 0, and C = 8
The discriminant is
.
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Because the discriminant is less than 0, B = 0 and A = C, the conic is a circle.
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The discriminant is
.
9-6 Identifying Sections Because the Conic discriminant is less than 0 and A ≠ C, the conic is an ellipse. 7. SOLUTION:
A = 8, B = 0, and C = 8
The discriminant is
.
Because the discriminant is less than 0, B = 0 and A = C, the conic is a circle. 9. SOLUTION:
A = 4, B = 8, and C = –8
The discriminant is
.
Because the discriminant is greater than 0, the conic is a hyperbola. 11. SOLUTION:
A = 8, B = 12, and C = 16
The discriminant is
.
Because the discriminant is less than 0 and A ≠ C, the conic is an ellipse.
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