Mathematics, 09.01.2020 06:31 emiliestinnett

11. a circle is given by the equation (x^2+2x+1)+(y^2+4y+4)=121.
a. what is the center of the circle?
b. what is the radius of the circle?
c. describe what you had to do in order to determine the center and the radius of the circle.

Answers: 3

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Answer from: skyemichellec

a) the centre of the circle is at point (h,k) = (-1,-2)

b) the radius of the circle is r = 11

c) we need to factorize each of the equation and write it in the form of the standard equation of a circle the we will compare to the standard equation of circle so as to get the values of the radius and the centre.

Step-by-step explanation:

Given;

Equation of the circle is

(x^2+2x+1) + (y^2+4y+4)=121

To determine the centre and radius of the circle we need to factorize each of the equation to give the

(x-h)^2 + (y-k)^2 = r^2 1

This is the standard form of a circle. We will then use this form to determine the center and radius of the circle. By Matching the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.

Factorizing the equation of the circle we have;

(x+1)^2 + (y+2)^2 = 11^2 2

Comparing equation 2 to 1

We have;

h = -1

k = -2

r = 11

Therefore,

a) the centre of the circle is at point (h,k) = (-1,-2)

b) the radius of the circle is r = 11

Answer from: Quest

Suredude why not right

Answer from: Quest

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒ $y=\frac{+1}{+1}x+0$

or $y=\frac{-1}{-1}x+0$

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

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11. a circle is given by the equation (x^2+2x+1)+(y^2+4y+4)=121.
a. what is the center of the...

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