Respuesta :

We know that a circle is a locus of points which keep equal distance from a fixed point known as centre and the fixed distance known as radius.

Here given that centre is (4,-5) and radius =2

let (x,y) be any point on the circle.

Then by definition of circle, we have distance between (x,y) and cenre will be the constant = 2.

i.e. using distance formula

[tex]\sqrt{(x2-x1)^2+(y2-y1)^2} = \sqrt{(x-4)^2+(y+5)^2} =2[/tex]

Square both the sides

[/tex]{(x-4)^2+(y+5)^2} =2^2[/tex]

Or

[/tex]{(x-4)^2+(y+5)^2} =4[/tex]

is the answer.


alinakincsem

Answer:

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

Step-by-step explanation:

We are given a circle with a radius of 2 with a center at the point (4, -5).

Assuming x and y to be the coordinates of any point on the circle, we can find the equation of the circle by using the following distance formula:

[tex]r=\sqrt{(x_1-x)^2+(y_1-y)^2}[/tex]

Putting the given values to get:

[tex]2=\sqrt{(x-4)^2+(y+5)^2}[/tex]

Taking square on both sides to get:

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

Therefore, the equation of the given circle with radius 2 and center at (4, -5) is [tex](x-4)^2+(y+5)^2=4[/tex].

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