Question

Draw a circle with an equation of x2 + 4x + y2 + 2y = 4. 5 4 3 2 1 -5 -4 -3 -2 -1 - 1 1 2 3 4 -2 -3 -4 -5 Clear All Draw:

Answer 1

The general equation of a circle is given by,

`(x-h)^2+(y-k)^2=r^2\text{ ----(1)}`

Here, (h, k) is the coordinates of the center of the circle and r is the radius of the circle.

The given equation of a circle is,

`x^2+4x+y^2+2y=4----(1)`

We have to convert equation (2) to the general form of the equation of a circle.

For that, first add constants on both sides of the equation.

`\begin{gathered} x^2+4x+4+y^2+2y+1=4+4+1 \\ x^2+2* x*2+2^2+y^2+2y*1+1^2=9 \end{gathered}`

Write the equation as sum of perfect squares in x and y.

`\begin{gathered} (x+2)^2+(y+1)^2=3^2\text{ } \\ (x-(-2))^2+(y-(-1))^2=3^2\text{ -----(3)} \end{gathered}`

Equation (3) is now in the form of equation (1). Comparing equations (1) and (3), we get

h=-2, k=-1 and r=3.

So, the center of the circle is at (-2, -1) and the radius of the circle is r=3.

Now, the circle can be plotted as: