Touch x-axis

Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.

Result

a = (Correct answer is: a=(x+2)^2+(y-2)^2=4) Wrong answer
b = (Correct answer is: b=(x-6)^2+(y-10)^2=100) Wrong answer

Solution:

(xm)2+(yn)2=r2  (m+2)2+(n4)2=r2 m2+(n2)2=r2 n=r  (m+2)2+(n4)2=n2 m2+(n2)2=n2  m2+4 m8 n+20=0 m24 n+4=0  n=(m2+4)/4   m2+4m8((m2+4)/4)+20=0  m2+4 m8 ((m2+4)/4)+20=0 m2+4m+12=0 m24m12=0  a=1;b=4;c=12 D=b24ac=4241(12)=64 D>0  m1,2=b±D2a=4±642 m1,2=4±82 m1,2=2±4 m1=6 m2=2   Factored form of the equation:  (m6)(m+2)=0  n1=(m12+4)/4=(62+4)/4=10  n2=(m22+4)/4=((2)2+4)/4=2  r=n  r=2,m=2,n=2 r=10,m=6,n=10   a=(x+2)2+(y2)2=4
b=(x6)2+(y10)2=100



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Showing 1 comment:
#
Math student
how do you end up with n=r ?

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