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:

(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 m  8 n + 20 = 0 m2  4 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=2ab±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+(y2)2=4

Our quadratic equation calculator calculates it.

b:b=(x6)2+(y10)2=100



Did you find an error or inaccuracy? Feel free to write us. Thank you!



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





Tips for related online calculators
Are you looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: