Question

write the equation of the circle in standard form. find the center, radius, intercepts, and graph the circle. x^2+y^2-6x-8y+25=36

Answer 1

x ^ 2 + y ^ 2 - 6 x - 8 y + 25 = 36


Equation of a circle in standard form :

( x - h ) ^ 2 + ( y - k ) ^ 2 = r ^ 2


x ^ 2 + y ^ 2 - 6 x - 8 y + 25 = 36

x ^ 2 - 6 x + y ^ 2 - 8 y + 25 = 36

( x ^ 2 - 6 x ) + ( y ^ 2 - 8 y ) + 25 = 36

The process involves completing the square separately for the x and y variables.


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( x - 3 ) ^ 2 = x ^ 2 - 2 * x * 3 + 3 ^ 2

( x - 3 ) ^ 2 = x ^ 2 - 6 x + 9 Subtract 9 to both sides

( x - 3 ) ^ 2 - 9 = x ^ 2 - 6 x + 9 - 9

( x - 3 ) ^ 2 - 9 = x ^ 2 - 6 x

x ^ 2 - 6 x = ( x - 3 ) ^ 2 - 9



( y - 4 ) ^ 2 = y ^ 2 - 2 * y * 4 + 4 ^ 2

( y - 4 ) ^ 2 = y ^ 2 - 8 y + 16 Subtract 16 to both sides

( y - 4 ) ^ 2 - 16 = y ^ 2 - 8 y + 16 -16

( y - 4 ) ^ 2 - 16 = y ^ 2 - 8 y

y ^ 2 - 8 y = ( y - 4 ) ^ 2 - 16

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( x ^ 2 - 6 x ) + ( y ^ 2 - 8 y ) + 25 = 36

( x - 3 ) ^ 2 - 9 + ( y - 4 ) ^ 2 - 16 + 25 = 36

(x - 3 ) ^ 2 + ( y - 4 ) ^ 2 - 25 + 25 = 36

( x - 3 ) ^ 2 + ( y - 4 ) ^ 2 = 36


( x - 3 ) ^ 2 + ( y - 4 ) ^ 2 = 6 ^ 2