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Give the equation for a circle with the given center and radius.
Center at (-1, 3), radius = 4
A. (x+3)2+(y−1)2=4
B. (x−3)2+(y+1)2=4
C. (x−1)2+(y+3)2=16
D. (x+1)2+(y−3)2=16

Respuesta :

Answer:

It is D. (x + 1)^2 + (y - 3)^2 = 16.

Step-by-step explanation:

The general equation of a circle is

(x - h)^2 + (y - k)^2 = r^2  where  the center is (h, k) and the radius is r.

So substituting the given values the required equation is:

(x + 1)^2 + (y - 3)^2 = 4^2.

Answer:

D. [tex](x+1)^2+(y-3)^2=16[/tex]

Step-by-step explanation:

We are asked to write equation of a circle whose center is at point [tex](-1,3)[/tex] and whose radius is 4 units.

We know that equation of a circle is standard form is in format [tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h,k)[/tex] is the center of circle.

Upon substituting [tex]h=-1[/tex], [tex]k=3[/tex] and [tex]r=4[/tex] in the standard form of circle, we will get:

[tex](x-(-1))^2+(y-3)^2=4^2[/tex]

[tex](x+1)^2+(y-3)^2=16[/tex]

Therefore, our required equation would be [tex](x+1)^2+(y-3)^2=16[/tex] and option D is the correct choice.

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