# Circle

Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q.

Write the equation of circle and determine the coordinates of the center and radius.

p: x-10 = 0
q: -x-19 = 0
a: 9x-4y+5 = 0

Correct result:

xS =  -4.5
yS =  -8.88
r =  NAN

#### Solution:

$A = p \cap a = [10; 0] \ \\ B = q \cap a = [-19; 0] \ \\ S = \dfrac{ AB }{2} = [-4.5; -8.88] \ \\ t \perp p ; t \perp q; S \in t \ \\ t: +y +1 = 0 \ \\ T = p \cap t = [10; NAN] \ \\$
$y_{ S }=(23.75+(-41.5))/2=- \dfrac{ 71 }{ 8 }=-8.88$
$r = |SA| = \sqrt{ (x_S-x_T)^2+(y_S-y_T)^2 } = NAN \ \\ \ \\ (x +4.5)^2+(x +8.88)^2 = NAN^2 \ \\$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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Showing 1 comment: Math student
Many examples required Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
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 quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

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