11'2 Points of Intersections

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11.2 Points of Intersections

• A circle is the set of al points equidistant from
  a fixed point, the center.
• The radius of a circle is the distance r
  between the center and any point on the circle.
• The standard equation for a circle
• x2 y2 r2 (x h)2 (y k)2 r2
• center (0, 0) center (h, k)
• radius r radius r
• Equation for finding r
• r sqrt (x 0)2 (y 0)2
• center (0, 0)

(square root)
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Example 1

• Given the point (2,5) and center (0,0), write the
  standard equation for a circle.

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Graphing a Circle

• Plot the given point in our case (2, 5) on a
  graph.
• Set the compass at the origin.
• Open the compass from the origin to the point.
• Draw a circle through the point.
• The distance from any point on the circle to the
  center will be the distance r, the radius.
• In our case, r sqrt (29) (approx) 5.4

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Intersections

• An intersection is when a point lies on more than
  one graph.
• For example, if a circle and line were sketched
  on the same graph, the point or points of
  intersection would be where the line and circle
  touch.
• Given two equations one for a circle, and one for
  a line to find the point(s) of intersection
• - Substitute the line equation into the circle
  equation.
• - Solve for x.
• - Use the value(s) found for x, and substitute
  back into the equation for the line.
• - Solve for y.
• - You will then have the ordered pair(s) that
  represent the points of intersection for the
  line and the circle.

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Example Intersection
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Graph