Question

Which equation represents a circle with the same center as the circle shown but with a radius of 2 units? (x – 4)2 (y – 5)2 = 2 (x – 4)2 (y – 5)2 = 4 (x – 5)2 (y – 4)2 = 2 (x – 5)2 (y – 4)2 = 4.

Answer 1

You can use the equation of the circle with center at (h,k) and the radius of f units.

The correct option for the given condition is

Option C: $(x-4)^2 + (y-5)^2 = 4$

What is the equation of the circle with the center at (h,k) and radius of r units?

If a circle has center at (h,k) and radius is of r units, then its equation is given as

$(x-h)^2 + (y-k)^2 = r^2$

How to form the equation of the circle with given conditions?

Since the graphed circle has center at x = 4 and y = 5, thus we have

(h,k) = (x coordinate of center, y coordinate of center ) = (4,5)

And since the radius of the needed circle is needed to be of 2 units, thus,

r = 2 units

Using the above specified  formula, we get the equation of the needed circle as

$(x-h)^2 + (y-k)^2 = r^2\\(x-4)^2 + (y-5)^2 = 2^2 = 4\\\\(x-4)^2 + (y-5)^2 = 4$

Thus,

The correct option for the given condition is

Option C: $(x-4)^2 + (y-5)^2 = 4$

Learn more about equation of circles here:

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