Using the distance formula: d = √[(4 - 1)² + (5 - 1)²] = √[9 + 16] = √25 = 5.

Using the distance formula: d = √[(1 - 1)² + (5 - 2)²] = √[0 + 9] = √9 = 3.

Using the distance formula: d = √[(2 - 6)² + (3 - 8)²] = √[16 + 25] = √41.

Using the distance formula: d = √((6 - 6)² + (2 - 8)²) = √(0 + 36) = √36 = 6.

The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|) = tan⁻¹(5/3), which is approximately 90 degrees.

Using the distance formula: d = √[(2 - (-1))² + (2 - (-1))²] = √[(2 + 1)² + (2 + 1)²] = √[9 + 9] = √18 = 3√2 ≈ 4.24.

Using the distance formula: d = √[(0 - 0)² + (8 - 0)²] = √[0 + 64] = √64 = 8.

Using the distance formula: d = √[(4 - 1)² + (6 - 2)²] = √[9 + 16] = √25 = 5.

Using the distance formula: d = √[(2 - 2)² + (-1 - 3)²] = √[0 + 16] = √16 = 4.

Using the formula for distance from a point to a line, the distance is |2(1) + 3(2) - 6| / sqrt(2^2 + 3^2) = 1.

Setting y = 0 in the equation gives 5x = 10, thus x = 2. The x-intercept is 2.

Setting x = 0 in the equation gives 2y = 10, thus y = 5. The y-intercept is 5.

Using the distance formula: d = √[(2 - (-1))² + (2 - (-1))²] = √[9 + 9] = √18 = 3√2.

Using the distance formula: d = √[(4 - (-2))² + (5 - (-3))²] = √[(4 + 2)² + (5 + 3)²] = √[36 + 64] = √100 = 10.

Using the distance formula: d = √[(6 - 0)² + (8 - 0)²] = √[36 + 64] = √100 = 10.

Using the distance formula: d = √[(4 - 1)² + (5 - 1)²] = √[9 + 16] = √25 = 5.

Using the distance formula: d = √[(3 - 3)² + (7 - 3)²] = √[0 + 16] = √16 = 4.

Using the distance formula: d = √((3 - 3)² + (1 - 7)²) = √(0 + 36) = √36 = 6.

Using the distance formula: d = √[(5 - 5)² + (1 - 5)²] = √[0 + 16] = √16 = 4.

The slope m = (7 - 3) / (4 - 2) = 2. Using point-slope form: y - 3 = 2(x - 2) gives y = 2x + 1.

Solving the equations simultaneously, we find the intersection point is (1, 1).

Solving the equations simultaneously, we find the intersection point is (3, 4).

The equation x^2 = -12y indicates that the parabola opens downwards.

In the equation x^2 = 4py, we have 4p = 16, thus p = 4. The distance from the vertex to the focus is 4.

The length of the latus rectum for the parabola x^2 = 4py is 4p. Here, p = 4, so the length is 8.

To find the y-intercept, set x = 0. The equation becomes y = -0^2 + 4(0) - 3 = -3.

'c' represents the y-intercept of the line, which is the point where the line crosses the y-axis.

Setting x = 0 in the equation gives y = 8. Thus, the y-intercept is -8.

Setting y = 0 in the equation gives 5x = 60, thus x = 12.

Rearranging to slope-intercept form gives y = -7/2x + 7, so the slope is -7/2.