how to solve circle equations

Question

1.  How do I write an equation of the circle with center (-2,3) and radius 8?

 

2.  How do I found the radius and center using the equation  of a circle x^2 + y^2 - 10x + 4y + 13 = 0 ?

 

3.  How do I found the equation of a parabola  with the vertex (0,0) and focus (0,4) ?

 

thanks

Answer 1

1)

 

   ( X +2 ) ^2 + ( Y -3 ) ^2 = 8^2

 

   ( X +2 ) ^2  + ( Y - 3 )^2  = 1

        64                 64

 

2) 

     X ^ 2 + Y ^2 -10x + 4Y +13 = 0

 

    X ^2 - 10X + 25 - 25 + Y^2 + 4Y  + 4 - 4 + 13 =0

 

   (  X - 5 ) ^2  + ( Y + 2 ) ^2 = 16

 

     ( X -5 ) ^2 + ( Y + 2 ) ^2 = 1

          16                16 

 

     Centre: ( 5 , -2 )   radius =4

 

 

Answer 2

How to solve circle equations
1. How do I write an equation of the circle with center (-2,3) and radius 8?
2. How do I found the radius and center using the equation of a circle x^2 + y^2 - 10x + 4y + 13 = 0 ?
3. How do I found the equation of a parabola with the vertex (0,0) and focus (0,4) ?

 

1)  The equation of a circle is (x-h)² + (y-k)² = r²  where (h,k) is the center of the circle and r is the radius.  The center is (-2,3) and the radius is 8.  Just plug those values into the equation.

 

2)  x² + y² - 10x + 4y + 13 = 0

 

Complete the squares for x and y:

 

(x²-10x+25) +(y²+4y+4) +13 - 25 - 4 = 0

 

(x-5)² + (y+2)² = 16

 

Center = (5,-2), Radius = √16 = 4

 

3) The vertex-focus form of a parabola is 4p(y-k)=(x-h)² where p = the distance from the vertex to the focus and (h,k) is the vertex.  You know the vertex is (h=0,k=0) and p=4.  Just plug those values into the equation.