Question

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.
x2 + 2x + y2 + 4y = 20


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Answer 1

Answer:  The required center of the given circle is (-1, -2) and radius is of length 5 units.

Step-by-step explanation:  We are given to find the center and the radius of the circle with the following equation :

$x^2+2x+y^2+4y=20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

the STANDARD equation of a circle with center (h, k) and radius of length r units is given by

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

From equation (i), we have

$x^2+2x+y^2+4y=20\\\\\Rightarrow (x^2+2x)+(y^2+4x)=20\\\\\Rightarrow (x^2+2\times x\times1\1^2)+(y^2+2\times y\times2+2^2)=20+1^2+2^2\\\\\Rightarrow (x+1)^2+(y+2)^2=20+1+4\\\\\Rightarrow (x+1)^2+(y+2)^2=25\\\\\Rightarrow (x-(-1))^2+(y-(-2))^2=5^2.$

Comparing the above equation with the standard form, we get

center, (h, k) = (-1, -2)  and radius, r = 5 units.

Thus, the required center of the given circle is (-1, -2) and radius is of length 5 units.

Answer 2

The center is at (-1,-2) and radius of 5
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