Conic Sections Circles

Conic Sections –Circles The coefficients of x 2 and y 2 n The coefficients of x 2 and y 2 have the same sign and same value. n An example of this is: x 2 + y 2 = 25 n It is easy to see that the coefficients for x 2 and y 2 are both equal to positive 1.

Conic Sections – Circles Coordinate Values of (h,k) n The point (h,k) represents the center of the circle. n In the example x 2 + y 2 = 25, the center is at: (h,k) = (0,0)

Conic Sections - Circles The radius of the circle n In the example x 2 + y 2 = 25 the length of the radius is the square root of 25. n The radius of this circle has a value, r = 5

Conic Sections – Circles Example # 1 - Graph it! n The quadratic relationship being graphed is x 2 + y 2 = 25 n The coefficients of x 2 and y 2 are both equal to positive one. This tells us this conic section is a CIRCLE. n Center (h,k) = (0,0) n Radius = 5

Conic Sections – Circles Example # 2 - Graph it! n The quadratic relationship being graphed is (x-2) 2 + (y+1) 2 = 25 n The coefficients of x 2 and y 2 are both equal to positive one. This tells us this conic section is a CIRCLE. n Center (h,k) = (2,-1) n Radius = 5

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