205k views
2 votes
Write the standard form of the equation of a circle with a radius of 2 and center at (4,-5)

Write the standard form of the equation of a circle with a radius of 2 and center-example-1
User Heff
by
8.2k points

2 Answers

1 vote

Answer:


(x-4)^2+(y+5)^2=4

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:


r=√((x_1-x)^2+(y_1-y)^2)

Putting the given values to get:


2=√((x-4)^2+(y+5)^2)

Taking square on both sides to get:


4=(x-4)^2+(y+5)^2

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

User Adisak
by
7.9k points
1 vote

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


√((x2-x1)^2+(y2-y1)^2) = √((x-4)^2+(y+5)^2) =2

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.


User Mike Driver
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories