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. \( r=5 ; \quad(h, k)=(-4,-3) \) The standard form of the equation of this circle is \( (x+4)^{2}+(y+3)^{2}=25 \). The general form of the equation of this circle is (Simplify your answer.)

We start with the standard form of a circle with center (h, k) and radius r:   (x – h)² + (y – k)² = r² Given h = –4, k = –3, and r = 5, the standard form becomes   (x + 4)² + (y + 3)² = 25 To express this in the general form, we expand and simplify the equation: 1. Expand (x + 4)² and (y + 3)²:   (x + 4)² = x² + 8x + 16   (y + 3)² = y² + 6y + 9 2. Combine the expansions:   x² + 8x + 16 + y² + 6y + 9 = 25 3. Combine like terms (16 + 9 = 25):   x² + y² + 8x + 6y + 25 = 25 4. Subtract 25 from both sides to write in general form:   x² + y² + 8x + 6y = 0 So, the general form of the equation is:   x² + y² + 8x + 6y = 0 Graphing the Circle: • Center: (–4, –3) • Radius: 5 Key points on the circle can be found by moving 5 units in the cardinal directions from the center:   – Rightmost point: (–4 + 5, –3) = (1, –3)   – Leftmost point: (–4 – 5, –3) = (–9, –3)   – Topmost point: (–4, –3 + 5) = (–4, 2)   – Bottommost point: (–4, –3 – 5) = (–4, –8) To sketch the graph:  1. Plot the center at (–4, –3).  2. Plot the four key points listed above.  3. Draw a smooth curve passing through these points to form the circle. This completes the answer: Standard form: (x + 4)² + (y + 3)² = 25 General form: x² + y² + 8x + 6y = 0