Equation of circle: (x-h)² + (y-k)² = r² => (x-3)² + (y+2)² = 5² = 25.

Standard form of a circle: (x-h)² + (y-k)² = r². Here, h=2, k=-3, r=5.

The directrix of the parabola x^2 = 4py is given by y = -p. Here, p = 3, so the directrix is y = -3.

The directrix of the parabola x^2 = 8y is y = -2.

The equation of the ellipse is x^2/25 + y^2/9 = 1.

Parallel lines have the same slope, so y - 4 = 2(x - 3) => y = 2x - 2.

Parallel lines have the same slope: y - 1 = 2(x - 1) => y = 2x - 1.

Parallel lines have the same slope, so y - 1 = 3(x - 1) => y = 3x - 1.

Parallel lines have the same slope. The slope is 3, so using point-slope form: y + 2 = 3(x - 0) => y = 3x - 2.

Since parallel lines have the same slope, the equation is y - 5 = 3(x - 2) which simplifies to y = 3x + 1.

Parallel lines have the same slope. Using point-slope form: y - 2 = 3(x - 1) gives y = 3x - 1.

The slope of the given line is 3. Using point-slope form: y - 5 = 3(x - 2) gives y = 3x + 1.

Since parallel lines have the same slope, the equation is y - 5 = 3(x - 2) which simplifies to y = 3x + 1.

Since parallel lines have the same slope, the equation is y - 1 = 3(x - 2) which simplifies to y = 3x - 5.

Parallel lines have the same slope. The slope is 3. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.

Since the lines are parallel, they have the same slope. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.

Parallel lines have the same slope. Using point-slope form: y - 3 = 4(x - 2) => y = 4x - 5.

Parallel lines have the same slope. Using point-slope form: y - 3 = 4(x - 2) => y = 4x - 8 + 3 => y = 4x - 5.

Parallel lines have the same slope. Using point-slope form: y - 3 = 5(x - 2) gives y = 5x - 7.

Slope = (4-0)/(2-0) = 2, so the equation is y = 2x.

Equation of line: y = mx + c; here m = 3, c = 0 => y = 3x

Using point-slope form: y - 3 = 2(x - 2) => y = 2x - 4 + 3 => y = 2x - 1.

The slope m = (4 - 2) / (3 - 1) = 1. Using point-slope form, y - 2 = 1(x - 1) gives y = x + 1.

The slope m = (6 - 2) / (3 - 1) = 2. Using point-slope form, y - 2 = 2(x - 1) gives y = 2x.

Direction ratios = (3, 3, 3), hence the line equation is x = 1 + 3t, y = 2 + 3t, z = 3 + 3t.

The slope of the perpendicular line is -1/3. Using point-slope form, we find y - 3 = -1/3(x - 2) which simplifies to y = -1/3x + 4.

The slope of the given line is 3, so the perpendicular slope is -1/3. Using point-slope form: y - 3 = -1/3(x - 2) gives y = -1/3x + 4.

The slope of the perpendicular line is -1/3. Using point-slope form: y - 3 = -1/3(x - 2) gives y = -1/3x + 4.

The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1) gives y = -1/3x + 4/3.

The slope of the given line is 3. The slope of the perpendicular line is -1/3. Thus, the equation is y = -1/3x.