Touch x-axis

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

Correct answer:

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

Step-by-step explanation:

(x−m)2+(y−n)2 = r2  (m+2)2+(n−4)2=r2 m2+(n−2)2=r2 n=r  (m+2)2+(n−4)2=n2 m2+(n−2)2=n2  m2 + 4 m − 8 n + 20 = 0 m2 − 4 n + 4 = 0  n = (m2+4)/4  m2+4m−8⋅ ((m2+4)/4)+20=0  m2+4 m−8⋅ ((m2+4)/4)+20=0 −m2+4m+12=0 m2−4m−12=0  a=1;b=−4;c=−12 D=b2−4ac=42−4⋅1⋅(−12)=64 D>0  m1,2​=2a−b±D​​=24±64​​ m1,2​=24±8​ m1,2​=2±4 m1​=6 m2​=−2  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:a=(x+2)2+(y−2)2=4

Our quadratic equation calculator calculates it.

b:b=(x−6)2+(y−10)2=100

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





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