Set y = 0 in the equation: 3x = 12 => x = 4.

Rearranging gives y = -3/4x + 3. The slope is -3/4.

Rearranging gives y = -3/4x + 3. The y-intercept is 3.

The slope of the line is given by -A/B = -3/-4 = 3/4. Parallel lines have the same slope.

Rearranging gives y = (3/4)x + 3, so the slope is -3/4.

Rearranging gives y = -5/12 x + 5, so the slope is -5/12.

Setting x = 0 in the equation gives 2y = 10, hence y = 5.

Reflecting about the x-axis changes the sign of y-coefficient: 5x + 2y + 10 = 0.

Slope of 2x + 3y = 6 is -2/3, so m = 3/2 (negative reciprocal).

The lines intersect if the discriminant D = b^2 - 4ac > 0.

The sum of the slopes of the lines can be found using the relation -b/a, which gives -3.

Using the formula for the angle between two lines, we can derive the coefficient of xy that satisfies the angle condition.

The product of the slopes of the lines can be found from the equation. Here, the product of the slopes is given by -c/a, where c is the coefficient of xy and a is the coefficient of x^2.

For the lines to be perpendicular, the condition 4 - 4(3)(2) = 0 must hold, leading to k = 0.

The product of the slopes of the lines represented by ax^2 + bxy + cy^2 = 0 is given by c/a. Here, c = 2 and a = 3, so the product is 2/3.

The lines are coincident when the determinant of the coefficients is zero, leading to k = 0.

The nature of the intersection can be determined by the slopes, which indicate that the angle is obtuse.

The angle can be found using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, where m1 and m2 are the slopes derived from the equation.

The sum of the slopes of the lines is given by -b/a, which is 0 in this case.

The nature of the roots can be determined by the discriminant of the quadratic equation.

The lines are not perpendicular as the condition for perpendicularity is not satisfied.

The condition for the lines to be real and distinct is that the discriminant D must be greater than 0.

For the lines to be perpendicular, the condition a + b = 0 must hold.

For the lines to be coincident, the constant term must be zero.

For the lines to be perpendicular, the condition a + b = 0 must hold.

For the lines to be perpendicular, the condition a*b + h^2 = 0 must hold.

Using the vertex form y = a(x - 1)^2 - 2 and substituting (0, 0), we get 0 = a(0 - 1)^2 - 2 => 2 = a => a = 2.

In the equation y^2 = 4px, we have 4p = 16, thus p = 4.

In the equation y^2 = 4px, we have 4p = 20, thus p = 20/4 = 5.

Slope = (4-2)/(3-1) = 1, and it remains the same for other points.