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Conic Sections - Circles

Consider two points C(h,k) and P(x,y) ;and the distance between them is r. From the distance formula:

square both sides
r2= ( x - h )2+ ( y - k )2

r2= ( x - h )2 + ( y - k )2 is the standard equation for circles.

Ax2+ Ay2+ Dx + Ey + F = 0
is the general form of the equation for circles.

ex.
Write the general equation of the circle with center at C(4,-5) and a
radius of 5.

r2= ( x - h )2+ ( y - k )2
52= ( x - 4 )2+ ( y -(-5))2
25 = x2 -8x + 16 + y2 + 10y + 25

x2+ y2 -8x + 10y + 16 = 0 is the general equation.


Find the center and the radius of the circle with equation x2+ y2-10x - 4y + 16 = 0.

x2+ y2-10x - 4y +16 = 0

(x-10x ) + (y- 4y ) = -16 complete the square.
(x2-10x + 25) + (y2- 4y + 4) = -16 + 25 + 4
( x -5)2 + ( y - 2 )2 = 13

The center is at (5, 2) and the radius is

If the constant term in the standard equation is positive, then a graph of a circle exist. If it is zero, a single point exist, If it is negative, there is no graph.

Subject: 
Algebra
Subject X2: 
Algebra

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