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McGraw Hill Glencoe Algebra 2, 2012

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McGraw Hill Glencoe Algebra 2, 2012 View details

5. Law of Cosines

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Exercise 50 Page 828

Use the discriminant of the equation by rewriting it in the form Ax^2+Bxy+Cy^2+Dx+Ey+F=0.

Circle

Practice makes perfect

We want to state whether the graph of the given equation is a parabola, a circle, an ellipse, or a hyperbola. To do so, we will rewrite it in the form Ax^2+ Bxy+ Cy^2+ Dx+ Ey+ F=0. Then we can determine its discriminant. Recall that missing terms have coefficient 0. x^2 + y^2 - 8x - 6y + 5 = 0 ⇕ 1x^2 + 0xy + 1y^2 + ( - 8)x + ( - 6)y + 5=0The discriminant of the equation can be found by evaluating B^2-4 A C. This will tell us which type of conic section we might have.

Discriminant	Conic Section
B^2-4AC<0; B=0 and A=C	Circle
B^2-4AC<0; either B≠ 0 or A≠ C	Ellipse
B^2-4AC=0	Parabola
B^2-4AC>0	Hyperbola

Let's calculate the discriminant of our equation.

B^2-4AC

SubstituteValues

Substitute values

0^2-4( 1)( 1)

▼

Simplify

Calculate power

0-4(1)(1)

a * 1=a

0 - 4

Subtract term

- 4

The discriminant is less than 0 and A = C, so the graph of the equation is a circle.

Subchapter links

Check Your Understanding p.825

Practice and Problem Solving p.826-827

H.O.T. Problems p.827

Standardized Test Practice p.828

Spiral Review p.828

Skills Review p.828