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# Circles

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• Discuss how the radius can be drawn from the center to any point on the circle.
• Stress that in a linear equation, no variables are squared. In the parabola equation only one variable is squared, while two are squared in the circle equation.
• Ax+BY=C Stress that linear equations have exponents of 1 on both the x and the y. With parabolas, either the x or the y has an exponent of 2. With circles, both x and y terms are squared. Also with circles, the coefficients (or denominators) are the same for x 2 and y 2 (You will see in another lesson that that is not true for ellipses.)
• ### Transcript

• 1. Next CONIC SECTIONS Parabola Circle Ellipse Hyperbola Quadratic Relations Previous Main Menu End
• 2. What are conics?
• Conics, or conic sections, are the intersection of a plane with an infinite double cone. If that plane cuts both cones, it is a hyperbola. If it is parallel to the edge of the cone, you get a parabola. If neither is the case, it is an ellipse. The ellipse is also a circle if the plane is perpendicular to the altitude of the cone.
• 3. Circle Â©National Science Foundation
• 4. Circle
• The Standard Form of a circle with a center at (0,0) and a radius, r, isâ€¦â€¦..
Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  center (0,0) radius = 2 Copyright Â©1999-2004 Oswego City School District Regents Exam Prep Center
• 5. Circles
• The Standard Form of a circle with a center at (h,k) and a radius, r, isâ€¦â€¦..
Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  center (3,3) radius = 2 Copyright Â©1999-2004 Oswego City School District Regents Exam Prep Center
• 6.
• Review: The geometric definition relies on a cone and a plane intersecting it
• Algebraic definition: a set of points in the plane that are equidistant from a fixed point on the plane (the center).
• 7.
• Find the distance from the center of the circle (h,k) to any point on the circle (represented by (x,y)). This is the radius of the circle.
• Review the distance formula:
• Substitute in the values.
• Square both sides to get
• the general form of a
• circle in center-radius form.
y x r (h,k) (x,y)
• 8.
• Center (h,k)
• 9.
• Both variables are squared.
• Equation of a circle in center-radius form:
• What makes the circle different from the a line?
• What makes the circle different from the parabola?
• 10.
• 11.
• 4. Write the equation of a circle centered at (2,-7) and having a radius of 5.
• (x - 2) 2 + (y + 7) 2 = 25
• 5. Describe (x - 2) 2 + (y + 1) 2 = 0
• A point at (2,-1)
• 6. Describe (x + 1) 2 + (y - 3) 2 = -1
• No graph
• 12.
• 7. Write the equation of a circle whose diameter is the line segment joining A(-3,-4) and B(4,3).
• What must you find first?
• The center and the radius.
• How can you find the center?
• The center is the midpoint of the segment.
• (Â½ , - Â½ )
• How can you find the radius?
• The radius is the distance from the center to a point on the circle. Use the distance formula.
• The equation is:
• 13.
• 8. Write in center-radius form and sketch:
• Hint: You must complete the square.
• 14.
• Whatâ€™s the standard form of a line?
• What are the steps for graphing a circle?
• How can you tell if the graph of an equation will be a line, a parabola, or a circle?