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Question

Find the standard equation of every circle that passes through the origin , has radius 5 , and is such thatthe y-coordinate of its center -4 ?

Answer 1

Always draw a picture for this kind of problem.....

You are given the y-coordinate of the center of one possible circle. The radius needs to be 5, so we can use the Pythagorean Theorem to get the x-coordinate: x = + or - 3

Using +3, the equation of this circle is"

(x - 3)² + (y + 4)² = 5²

Again using the Pythagorean Theorem, recognize that the squares of the x and y offsets must always add up to 25

Call the offsets A and B:

A² + B² = 25

Let's make out final equation a function of A: This means we need B as a function of A:

B² = 25 - A²

B = ±√(25 - A²)

Now we can write:

(x + A)² + (y ±√(25 - A²)² = 25

Use a graphing calculator or online graphing tool to verify that this is correct