Conics - Circle

Lessons

1. graphing a circle
   Sketch each circle and state the:
   i) center
   ii) radius
   
   1. ${\left( {\frac{{x - 5}}{3}} \right)^2} + {\left( {\frac{{y + 4}}{3}} \right)^2} = 1$
   2. ${x^2} + {y^2} = 25$
2. converting a circle equation to conics form by "completing the square"
   $4{x^2} + 4{y^2} + 24x - 8y + 15 = 0$
   1. Convert the equation to conics form.
   2. Sketch the graph and state the:
      i) center
      ii) radius
3. finding the equation of a circle given its properties
   Find the equation of a circle with:
   1. center $\left( { - 3,\;5} \right)$, radius = 7
   2. center $\left( {2,\;0} \right)$, passing through the point $\left( { - 1,\;4} \right)$
   3. diameter with endpoints $\left( { - 9,\;4} \right)$ and $\left( {15,\; - 6} \right)$
   4. center $\left( { - 2,\; - 1} \right)$, tangent to the line $3x + 4y = 15$