Solving Systems of Conics Algebraically

The video tutorial explains how to solve systems of conics algebraically, focusing on using substitution to find intersection points. It covers two examples: the intersection of a circle and a line, and the intersection of two parabolas. The tutorial provides step-by-step instructions on simplifying equations, substituting variables, and solving for intersection points, emphasizing the importance of finding both x and y coordinates to determine the points of intersection.

What are the two methods mentioned for solving systems of conics algebraically?

• Graphing and Factoring

• Elimination and Graphing

• Substitution and Elimination

• Completing the Square and Substitution

What is the simplified form of the circle equation 2x^2 + 2y^2 = 52?

• 2x^2 + 2y^2 = 26

• x^2 + y^2 = 52

• x^2 + y^2 = 13

• x^2 + y^2 = 26

After substituting y = x - 4 into the circle equation, what is the resulting equation?

• 2x^2 + 2(x - 4)^2 = 52

• x^2 + y^2 = 26

• x^2 + 2(x - 4) = 26

• x^2 + (x - 4)^2 = 26

What are the x-coordinates of the intersection points found in the first example?

• 2 and -2

• 3 and -3

• 4 and -4

• 5 and -1

What is the y-coordinate when x = 5 for the intersection of the circle and line?

• 1

• 5

• -5

• 0

What is the y-coordinate when x = -1 for the intersection of the circle and line?

• 1

• -5

• 0

• 5

In the second example, what shapes are being analyzed for intersection?

• Two parabolas

• A parabola and a line

• A circle and a line

• Two circles

What is the equation of the first parabola in the second example?

• y = x - 4

• x^2 + y^2 = 26

• y = x^2 - 4x + 4

• x^2 = y

What is the x-coordinate of the intersection point found in the second example?

• 1

• 0

• -1

• 2

What is the ordered pair of the intersection point between the two parabolas?

• (1, 1)

• (0, 0)

• (-1, -1)

• (2, 2)