Question 184089
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The equation of a circle with center at (<i>h</i>,<i>k</i>) and radius <i>r</i> is:


*[tex \LARGE \text{          }\math (x - h)^2 + (y - k)^2 = r^2]


You are given the center, (4,-7), and that the circle is tangent to the <i>y</i>-axis.  That means the radius is the distance from the <i>y</i>-axis to the center, or simply the value of the <i>x</i>-coordinate of the center, namely 4.  Substituting:


*[tex \LARGE \text{          }\math (x - 4)^2 + (y + 7)^2 = 16]



{{{drawing(
500, 500, -1, 12, -12, 1,
grid(1),
circle(4,-7,4),
circle(4,-7,.1),
locate(4.1,-7.1,C(4,-7)),
circle(0,-7,.1),
locate(.1,-7.1,T(0,-7))
blue(line(-.1,-7,-.1,-6)),
blue(line(4,-7,4,-6)),
blue(line(0,-6.5,4,-6.5)),
locate(2,-6,r=4)
)}}}


<i>T</i> is the point of tangency.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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