Respuesta :

Answer:

(x + 1)^2 + (y - 5)^2 = 26.

Step-by-step explanation:

The general form of the equation of a circle is:

(x - a)^2 + (y - b)^2 = r^2 where  the center is at  (a, b) and r is the radius.

Here a = -1 and b = 5.

The radius of this circle is the length from (-1, 5) to (4, 4) so we can work out r^2 which is:

r^2 = (-1-4)^2 + (5-4)^2

r^2 = 26.

So substituting for a, b and r in the general form the equation of the circle is

(x + 1)^2 + (y - 5(^2 = 26.

Answer:

[tex](x+1)^2+(y-5)^2=26[/tex]

Step-by-step explanation:

The standard form of an equation for a circle is:

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

where the center is (h,k) and the radius is r.

We are given (h,k)=(-1,5):

[tex](x--1)^2+(y-5)^2=r^2[/tex]

[tex](x+1)^2+(y-5)^2=r^2[/tex]

We can use (x,y)=(4,4) to find the value for [tex]r^2[/tex].

[tex](4+1)^2+(4-5)^2=r^2[/tex]

[tex](5)^2+(-1)^2=r^2[/tex]

[tex]25+1=r^2[/tex]

[tex]26=r^2[/tex]

So the equation for the circle is:

[tex](x+1)^2+(y-5)^2=26[/tex]

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