Algebra 2 CH 8.3 Graph and Write Equations of Circles.notebook
Algebra 2 CH 8.3 Graph and Write Equations of Circles.notebook
Graph and Write Equations of Circles
May 06, 2015
Graph and Write Equations of Circles Circle (boundary)
Radius
8.3 Graph and Write Equations of Circles • • • • •
r
circle center radius equation of a circle equation of a line tangent to a circle.
Center
Feb 83:43 PM
Graph and Write Equations of Circles Definition: A circle is the set of all points ( x , y ) that are equidistant from a fixed point, called the center of the circle.
Feb 83:43 PM
Feb 83:43 PM
Graph and Write Equations of Circles
Equation of a circle with a center at ( 0, 0 )
Feb 83:43 PM
Graph and Write Equations of Circles
Graph and Write Equations of Circles
Write the equation of a circle centered at ( 0 , 0 ) with a radius of 6.
What is the radius of the circle with an equation:
Feb 83:43 PM
Feb 83:43 PM
1
Algebra 2 CH 8.3 Graph and Write Equations of Circles.notebook
Graph and Write Equations of Circles
May 06, 2015
Graph and Write Equations of Circles
What is the radius of the circle with an equation:
Feb 83:43 PM
Graph and Write Equations of Circles
If the point ( 3 , 9 ) is on the circle, what is the radius?
Feb 83:43 PM
Graph and Write Equations of Circles If the point ( 3 , 9 ) is on the circle, what is the equation of the circle? We just found r2 = 90, so
x2 + y2 = 90
Feb 83:43 PM
Graph and Write Equations of Circles
Graph and Write Equations of Circles Is the point (1, 4) in the interior , exterior or on the boundary of the circle x2 + y2 =20 ? Pull
A circle has an interior , exterior and boundary. The boundary is the circle itself.
Feb 83:43 PM
Feb 83:43 PM
Feb 83:43 PM
2
Algebra 2 CH 8.3 Graph and Write Equations of Circles.notebook
May 06, 2015
Graph and Write Equations of Circles
Graph and Write Equations of Circles
Find the equation of the line tangent to the circle at the given point.
What is the equation of the tangent (red line)?
We need to do three things: • Find the slope of the radius at the given point. • Find the slope of the tangent line at the given point. • Substitute the information that we have into the pointslope equation of a line.
Feb 83:43 PM
Graph and Write Equations of Circles
Find the slope from the origin to (3,2)
Feb 83:43 PM
Graph and Write Equations of Circles
Feb 83:43 PM
Graph and Write Equations of Circles We have the slope of the radius, but the tangent line is perpendicular to the radius, so we now need to find the slope of the tangent line.
Feb 83:43 PM
Graph and Write Equations of Circles
Now we have a slope and a point so we will use the point slope form to write the equation of the line tangent to the circle that passes through the point (3,2).
Feb 83:43 PM
Feb 83:43 PM
3
Algebra 2 CH 8.3 Graph and Write Equations of Circles.notebook
Graph and Write Equations of Circles
May 06, 2015
Graph and Write Equations of Circles Find the equation of the line tangent to the circle at the given point.
Feb 83:43 PM
Graph and Write Equations of Circles
Feb 83:43 PM
Graph and Write Equations of Circles
slope of radius =
slope of tangent line =
equation of tangent line:
Feb 83:43 PM
Feb 83:43 PM
Graph and Write Equations of Circles 8.3 Graph and Write Equations of Circles • • • • •
circle center radius equation of a circle equation of a line tangent to a circle.
Feb 83:43 PM
4
Attachments
CH 8.3 Circle.gsp
Graph and Write Equations of Circles
May 06, 2015
Graph and Write Equations of Circles Circle (boundary)
Radius
8.3 Graph and Write Equations of Circles • • • • •
r
circle center radius equation of a circle equation of a line tangent to a circle.
Center
Feb 83:43 PM
Graph and Write Equations of Circles Definition: A circle is the set of all points ( x , y ) that are equidistant from a fixed point, called the center of the circle.
Feb 83:43 PM
Feb 83:43 PM
Graph and Write Equations of Circles
Equation of a circle with a center at ( 0, 0 )
Feb 83:43 PM
Graph and Write Equations of Circles
Graph and Write Equations of Circles
Write the equation of a circle centered at ( 0 , 0 ) with a radius of 6.
What is the radius of the circle with an equation:
Feb 83:43 PM
Feb 83:43 PM
1
Algebra 2 CH 8.3 Graph and Write Equations of Circles.notebook
Graph and Write Equations of Circles
May 06, 2015
Graph and Write Equations of Circles
What is the radius of the circle with an equation:
Feb 83:43 PM
Graph and Write Equations of Circles
If the point ( 3 , 9 ) is on the circle, what is the radius?
Feb 83:43 PM
Graph and Write Equations of Circles If the point ( 3 , 9 ) is on the circle, what is the equation of the circle? We just found r2 = 90, so
x2 + y2 = 90
Feb 83:43 PM
Graph and Write Equations of Circles
Graph and Write Equations of Circles Is the point (1, 4) in the interior , exterior or on the boundary of the circle x2 + y2 =20 ? Pull
A circle has an interior , exterior and boundary. The boundary is the circle itself.
Feb 83:43 PM
Feb 83:43 PM
Feb 83:43 PM
2
Algebra 2 CH 8.3 Graph and Write Equations of Circles.notebook
May 06, 2015
Graph and Write Equations of Circles
Graph and Write Equations of Circles
Find the equation of the line tangent to the circle at the given point.
What is the equation of the tangent (red line)?
We need to do three things: • Find the slope of the radius at the given point. • Find the slope of the tangent line at the given point. • Substitute the information that we have into the pointslope equation of a line.
Feb 83:43 PM
Graph and Write Equations of Circles
Find the slope from the origin to (3,2)
Feb 83:43 PM
Graph and Write Equations of Circles
Feb 83:43 PM
Graph and Write Equations of Circles We have the slope of the radius, but the tangent line is perpendicular to the radius, so we now need to find the slope of the tangent line.
Feb 83:43 PM
Graph and Write Equations of Circles
Now we have a slope and a point so we will use the point slope form to write the equation of the line tangent to the circle that passes through the point (3,2).
Feb 83:43 PM
Feb 83:43 PM
3
Algebra 2 CH 8.3 Graph and Write Equations of Circles.notebook
Graph and Write Equations of Circles
May 06, 2015
Graph and Write Equations of Circles Find the equation of the line tangent to the circle at the given point.
Feb 83:43 PM
Graph and Write Equations of Circles
Feb 83:43 PM
Graph and Write Equations of Circles
slope of radius =
slope of tangent line =
equation of tangent line:
Feb 83:43 PM
Feb 83:43 PM
Graph and Write Equations of Circles 8.3 Graph and Write Equations of Circles • • • • •
circle center radius equation of a circle equation of a line tangent to a circle.
Feb 83:43 PM
4
Attachments
CH 8.3 Circle.gsp
