Question 534153
determine the equation of the circle whose center is at (4,5) and tangent to the circle whose equation is x^2+y^2+4x+6y-23=0
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Find the center of x^2+y^2+4x+6y-23=0
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x^2+y^2+4x+6y = 23
{{{x^2 + 4x + 4 + y^2 + 6y + 9 = 23 + 4 + 9 = 36}}}
{{{(x+2)^2 + (y+3)^2 = 6^2}}}
Center at (-2,-3), r = 6
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Find the distance from the center to (4,5)
{{{d = sqrt(diffy^2 + diffx^2) = sqrt(8^2 + 6^2) = 10}}}
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The radius of the 2nd circle is 4, 10-6
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--> {{{(x-4)^2 + (y-5)^2 = 16}}}