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How do you find the center and radius of #(x - 5) ^2 + (y + 3)^ 2 = 25#?

Answer 1

centre = (5 ,-3) and radius = 5

The standard form of the equation of a circle is.

#color(red)(bar(ul(|color(white)(a/a)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(a/a)|)))# where (a ,b) are the coordinates of the centre and r, the radius.

#(x-5)^2+(y+3)^2=25" is in this form"#

and by comparison with the standard form.

#a=5,b=-3" and " r^2=25rArrr=sqrt25=5#

Hence centre = (5 ,-3) and radius = 5

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Answer 2

Elijah Allen

The center of the circle can be found by taking the opposite of the numbers being added to (x) and (y) inside the parentheses, so the center of the circle is at ((5, -3)). The radius of the circle is the square root of the number on the right side of the equation, so the radius is (5). Therefore, the center of the circle is ((5, -3)) and the radius is (5).

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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.