Question 1047542
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Find the equation of the circle (in general form) tangent to the line 4x + 5y = 7 and concentric with the circle. (x-4)^2 +y^2 -5=0
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<pre>
The center of the circle (of both circles) is at the point (4,0).


Find the distance from the point (4,0) to the straight line 4x + 5y = 7.
For it, use the formula for the distance from the point to the straight line in a coordinate plane

(for example, from the lesson <A HREF=https://www.algebra.com/algebra/homework/Vectors/The-distance-from-a-point-to-a-straight-line-in-a-coordinate-plane.lesson>The distance from a point to a straight line in a coordinate plane</A> in this site).

d = {{{abs(4*4 + 5*0 -7)/sqrt(4^2+5^2)}}} = {{{9/sqrt(41)}}}.

    (Do not miss "d" with the diameter! In opposite, the "d" is the radius:

        r = {{{9/sqrt(41)}}},  and  {{{r^2}}} = {{{81/41}}}. )

Now the equation of the circle is 

    {{{(x-4)^2 +y^2}}} = {{{81/41}}}.
</pre>

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{{{graph( 330, 330, -2.5, 7.5, -5.5, 4.5,
          sqrt(-(x-4)^2 + 81/41), -sqrt(-(x-4)^2 + 81/41), (7-4x)/5
)}}}


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Figure

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