The Circle and the Parabola

1
The Circle and the Parabola

• Section 7.1

2
Conic Sections

• Second degree equations in x and y have the form
  Ax2 Bxy Cy2 Dx Ey F 0
• A, B, and C cannot all be zero
• The graphs of the equations can be a point, a
  pair of lines, a circle, a parabola, an ellipse,
  a hyperbola, or no graph at all.
• These graphs are called conic sections.

3
Circles

• A circle is a set of a points that are a fixed
  distance from a point called the center. The
  fixed distance is called the radius.
• The standard equation of a circle with center (h,
  k) and radius r is

4
More on Circles

• The standard equation of a circle with center (0,
  0) and radius r is
• The general form of the equation of a circle is
  
• where c, d and e are real numbers.
• This equation is obtained by squaring the
  binomials in the standard equation with center
  (h, k),

5
Graph the circle whose equation is x2 y2 6x
2y -6.
6
Parabola

• A parabola is the set of points in a plane
  equidistant from a line l, the directrix, and a
  fixed point F, the focus, that is not on the
  line.
• The point on the parabola closest to the
  directrix is the vertex and the line passing
  through the vertex and the focus is the axis.

7
Standard Equation of a Parabola with Vertex at
(h, k)

• The standard equation of a parabola with vertex
  at (h, k) and opening to the right is
• (y k) 2 4p (x h)
• Where p is the distance from the vertex to the
  focus.
• If the vertex is at the origin the equation
  becomes y 2 4px

8
Standard equations of Parabola pgt 0
9
Find the equation of the parabola with vertex at
(0,0) and focus at (0,5)
10
Find the equation of the parabola with vertex at
(3,5) and focus at (3,2)
11
Find the equation of the parabola with vertex at
(-4,6) and passes through (0,3)
12
Change x2 2y 2x -7 to standard form and
graph it