1. Given (11,7) and (x,−5), find all x such that the distance between these two points is 13. Separate multiple answers with a comma. 2. Find the standard form of the equation for the circle with the following properties.

Center (8,−7/3) and tangent to the y-axis

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  1. x = {6, 16}

  2. (x -8)² +(y +7/3)² = 64

Step-by-step explanation:

1. The distance formula is useful for this.

  d² = (x2 -x1)² +(y2 -y1)²

  13² = (x -11)² +(-5 -7)² . . . . . . . . fill in the given point coordinates

  169 -144 = (x -11)² = 25 . . . . . . subtract 144

  x -11 = ±5 . . . . . . . . . . . . . . . . . take the square root

  x = 11 ±5 = {6, 16} . . . . . . . . . . add 11

The values of x that make the points 13 units apart are 6, 16.

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2. The standard form equation of a circle is ...

  (x -h)² +(y -k)² = r² . . . . . . circle centered at (h, k) with radius r

In order for the circle to be tangent to the y-axis, the radius must be equal to the distance the center is from the y-axis: the x-coordinate of the center point. That is, r = 8.

  (x -8)² +(y +7/3)² = 64