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What is the equation of a circle with center (1, -4) and radius 2?

A. (x-1)^2 + (y+4)^2 = 4
B. (x-1)^2 - (y+4)^2 = 4
C. (x-1)^2 + (y+4)^2 = 2
D. (x+1)^2 + (y-4)^2 = 4

Respuesta :

Yang100

Answer:

A) (x-1)^2+(y+4)^2=4

Step-by-step explanation:

Here's the equation of a circle with center and radius:

(x-h)^2+(y-k)^2=r^2 with the center being at the point (h, k)

and the radius being r.

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

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

The equation of a circle with center (1, -4) and radius 2 is (x-1)²+(y+4)²=4

The correct option is (A).

What is equation of circle?

The equation of circle represents the locus of point whose distance from a fixed point is a constant value. This fixed point is called the center of the circle and the constant value is the radius of the circle.

The standard equation of circle with center at (x1,y1)  and radius r is (x−x1)²+(y−y1)²=r².

We know equation of circle,

(x-a)²+(y-b)²=r²

Here, a=1, b=-4 and r=2

So,

(x-1)²+(y-(-4))²= 2²

(x-1)²+(y+4)²=4

Hence, the equation of circle is: (x-1)²+(y+4)²=4

Learn more about equation of circle here:

https://brainly.com/question/10618691

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