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How do you find the radius of a circle with equation #(x-5)^2+(y-3)^2=r^2# that contains the point at (5,1)?

Answer 1

Sophia Alfred

The radius will measure #2# units.

Since #(x, y) = (5, 1)#, we have:

#(5 - 5)^2 + (1 - 3)^2 = r^2#

#0^2 + (-2)^2 = r^2#

#4 = r^2#

#r = 2#

Here is the corresponding graph.

graph{(x - 5)^2 + (y -3)^2 = 2^2 [-10, 10, -5, 5]}

Hopefully this helps!

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Answer 2

Jayden Jackson

To find the radius of the circle, substitute the coordinates of the given point (5,1) into the equation of the circle and solve for ( r ).

( (5-5)^2 + (1-3)^2 = r^2 )

( 0 + (-2)^2 = r^2 )

( 4 = r^2 )

( r = \sqrt{4} )

( r = 2 )

So, the radius of the circle is ( 2 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.