Question

write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). then graph the circle.
r = 1; (h,k)=(-4,-3)
the standard form of the equation of this circle is (x + 4)^2+(y + 3)^2 = 1. (type your answer in standard form.)
the general form of the equation of this circle is . (simplify your answer. type an equation.)

Explanation:

Step1: Expand the standard - form equation

The standard - form of a circle is \((x - h)^2+(y - k)^2=r^2\). Here, \(h=-4\), \(k = - 3\), and \(r = 1\), so the standard form is \((x + 4)^2+(y+3)^2=1\). Expand \((x + 4)^2\) and \((y + 3)^2\) using the formula \((a + b)^2=a^{2}+2ab + b^{2}\).
\((x + 4)^2=x^{2}+8x + 16\) and \((y + 3)^2=y^{2}+6y+9\).
So, \((x + 4)^2+(y + 3)^2=1\) becomes \(x^{2}+8x + 16+y^{2}+6y + 9=1\).

Step2: Simplify to get the general form

Combine like - terms: \(x^{2}+y^{2}+8x + 6y+16 + 9-1=0\).
\(x^{2}+y^{2}+8x + 6y+24=0\).

Answer:

\(x^{2}+y^{2}+8x + 6y + 24=0\)