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Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units?

(x – 9)2 + (y + 4)2 = 25
(x + 4)2 + (y – 9)2 = 25
(x – 9)2 + (y + 4)2 = 100
(x + 4)2 + (y – 9)2 = 100

Respuesta :

Answer:

(x + 4)^2 + (y – 9)^2 = 25

Step-by-step explanation:

The standard form for a circle is

[tex](x - h)^{2} + (y - k)^{2} = r^{2}[/tex]     where (h, k) is the center and r is the radius

In your case, h = -4 and k = 9 and r = 5

So, (x + 4)^2 + (y – 9)^2 = 25

The equation for this circle is given as

[tex](x+4)^2 + (y-9)^2 = 25[/tex]

Data

  • h = -4
  • k = 9
  • r = diameter/2 = 10/2 = 5

Equation of Circle

The equation of circle is given by

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Let's substitute our values and get our equation

[tex](x--4)^2 + (y-9)^2 = 5^2\\(x+4)^2 + (y-9)^2 = 25[/tex]

we substituted the values of h and k and made sure it's in the standard form of equation of a circle.

The equation for this circle is given as

[tex](x+4)^2 + (y-9)^2 = 25[/tex]

This looks exactly like

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Learn more on equation of a circle here;

https://brainly.com/question/15214797

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