Write the standard form of the Equation of the circle with the following Center (5,7) and r= 4
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The standard form of the equation of a circle is
`(x-h)^2 + (y-k)^2 =r^2`
Fill in the values given for the center of the circle, h and k, as well as the radius given by r.
`(x-5)^2 + (y-7)^2 = 4^2`
`(x-5)^2 + (y-7)^2 =16`
`` Squaring an expression is the same as multiplying the expression by itself twice.
`(x-5)(x-5) +(y-7)^2 =16`
Use FOIL.
`(x^2 -10x+25) +(y-7)^2 =16`
`(x^2 -10x+25) + (y-7)(y-7) =16`
Use FOIL
`(x^2 -10x+25) + (y^2-14y+49) =16`
Combine like terms and reorder the polynomial.
`x^2-10x+y^2 -14y+74=16`
The equation of the circle with center (5,7) and radius 4 is
x^2-10x+y^2-14y+74=16.
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