Question

ra Q5 What is the equation of the circle represented by the graph below? O x² + y² + 8x + 4y -4 = 0 2 0 x2 + y2 + &r – 4y + 16 = 0 Or? + y2 - 8x +4y +4 = 0 0 6 А x2 + y2 - 8x – 4y - 16 = 0 -6 arch og a

Answer 1

The general equation of a circle is:

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

where (h, k) is the center and r is the radius.

From the graph, the center is located at (4, -2), that is, h = 4, and k = -2. And the radius is 4, that is, r = 4. Substituting into the general equation, we get:

$\begin{gathered} (x-4)^2+(y-(-2))^2=4^2 \\ (x-4)^2+(y+2)^2=16 \end{gathered}$

Solving the square of the binomials, and combining similar terms:

$\begin{gathered} \lbrack x^2+2\cdot x\cdot(-4)+(-4)^2\rbrack+\lbrack y^2+2\cdot y\cdot2+2^2\rbrack=16 \\ x^2-8x+16+y^2+4y+4-16=0 \\ x^2+y^2-8x+4y+(16+4-16)=0 \\ x^2+y^2-8x+4y+4=0 \end{gathered}$