Standard Form of Equation of Circle

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 1, Section 1.4

Find the standard form of the equation of each circle.

38. Center (-3, 1) and tangent to the y-axis.

42. Center (4, -2) and tangent to the line x = 1.

[Math Tutor]

The trick with tangent lines is that the radius is just the perpendicular distance from the center to the line.

38. Center [tex](-3, 1)[/tex], tangent to the y-axis (which is the line [tex]x = 0[/tex]). The distance from the center to the y-axis is the absolute value of its x-coordinate:
[tex]r = |-3| = 3[/tex]
Answer: [tex](x + 3)^2 + (y - 1)^2 = 9[/tex]

42. Center [tex](4, -2)[/tex], tangent to the vertical line [tex]x = 1[/tex]. Same idea, just measure horizontally:
[tex]r = |4 - 1| = 3[/tex]
Answer: [tex](x - 4)^2 + (y + 2)^2 = 9[/tex]

If it helps, sketch it. The circle only touches the line at one point, so the shortest distance from center to line is exactly the radius. For a vertical line you only care about the x-values, and for a horizontal line you would only care about the y-values.