Presentation on theme: "Circles Graphing and Writing Equations What is a circle? A conic formed when …. A second degree equation… A locus of points…"— Presentation transcript:
Circles Graphing and Writing Equations
What is a circle? A conic formed when …. A second degree equation… A locus of points…
Definition as a conic A circle is a conic or a conic section because it is formed by the intersection of a plane and a double-napped cone.
Algebraic Definition A circle is defined as the second degree equation Ax 2 +Bxy+Cy 2 +Dx+Ey+F = 0 when A = C.
But, what is a locus…? A locus is the set of all points, and only those points, that satisfy one or more conditions. So, A locus of points in a plane 10 cm from a point A gives a geometric description of a circle with center A and a radius of 10 A circle is a locus of points…..
Geometric Definition A circle is the locus or collection of all points (x, y) that are equidistant from a fixed point, (h, k) called the center of the circle. The distance r, between the center and any point on the circle is the radius
the standard form of a circle. (x- h) 2 + (y- k) 2 = r 2 where, center = (h, k) and radius = r Using the distance formula, you can derive
Equation of a circle : Practice ProblemsPractice Problems to write the equation of a circle when given the center and the radius.
What if the center and radius are not given? Try these : 1.Center = (0,3) and solution point = (0, 6) 2.Endpoints of diameter are (-2,3) and (6,5) 3.Center on the line y = 2, and tangent to the x-axis at (3,0)
Graph the circle To graph a circle, locate all the points that are a fixed distance r, from the center (h, k). Click here Click here to graph a circle
Graph a circle with center at the origin Example: Graph x 2 + y 2 = 4
To Graph a Circle center (h,k) and radius r Click Here Click Here To graph a circle if given a radius and a center Example: (x-3) 2 + (y-3) 2 =4
What are some applications? 1.Circular orbits of the earth for satellites. 2.Perfect shape for cross-section of a submarine. 3.Gears 4.Other