Question

Find the equation of the circle with center at (-1, -4) and radius of 2.

Answer 1

Answer:

the equation of the circle is (x + 1)^2 + (y + 4)^2 = 4 :)

Answer 2

Answer:  The required equation of the circle is $x^2+y^2+2x+8y+13=0$

Step-by-step explanation:  We are given to find the equation of the circle with center (-1, -4) and radius of length 2 units.

We know that

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

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

For the given circle,

center, (h, k) = (-1, -4)  and  radius, r = 2 units.

So, from equation (i), we get

$(x-(-1))^2+(y-(-4))^2=2^4\\\\\Rightarrow (x+1)^2+(y+4)^2=4\\\\\Rightarrow x^2+2x+1+y^2+8y+16=4\\\\\Rightarrow x^2+2x+y^2+8y+17-4=0\\\\\Rightarrow x^2+y^2+2x+8y+13=0$

Thus, the required equation of the circle is $x^2+y^2+2x+8y+13=0$