Question

A circle is centered at the point

(−2,5) and has a radius of 7 units.

Which points on the circle have an x-coordinate of 0? (Your answer should be a list of points, such as "(1,1), (2,4)".)


Which points on the circle have a y-coordinate of 2? (Your answer should be a list of points, such as "(1,1), (2,4)".)



Write an equation for the graph of this circle.

Answer 1

A circle is centered at the point

(−2,5) and has a radius of 7 units.

Which points on the circle have an x-coordinate of 0? (Your answer should be a list of points, such as "(1,1), (2,4)".)

Which points on the circle have a y-coordinate of 2? (Your answer should be a list of points, such as "(1,1), (2,4)".)

Write an equation for the graph of this circle.

Answer 2

• See below

Explanation:

Given:

• The radius is 7 and
• Center is at (- 2, 5).

The equation is:

• (x - h)² + (y - k)² = r² or
• (x + 2)² + (y - 5)² = 7² or
• (x + 2)² + (y - 5)² = 49

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The points with x = 0:

• (0 + 2)² + (y - 5)² = 49
• (y - 5)² = 49 - 4
• (y - 5)² = 45
• y - 5 = ± √45
• y = 5 ± √45
• y = 5 ± 3√5

The points are:

• (0, 5 + 3√5), (0, 5 - 3√5)

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The points with y = 2:

• (x + 2)² + (2 - 5)² = 7²
• (x + 2)² = 49 - 9
• (x + 2)² = 40
• x + 2 = √40
• x = - 2 ± 2√10

The points are:

• (- 2 + 2√10, 2), (- 2 - 2√10, 2)