Answer to Question #57671 in Analytic Geometry for sanjiv

Question

Write the general equation of the line satisfying the given conditions:
1. passing trough (1, 0) and parallel to the line through (1/2, 3) and (0,0)
2. passing through (2, -4) and parallel to the line 3x - 7y - 11 = 0
3. passing through (-1/3, 1/2) and perpendicular to the line through (4, 1) and (-2, 7)
4. passing through (-1/2, 2) and perpendicular to the line with slope -5/2
5. passing through the point of intersection of lines 5x - 2y - 12 = 0 and x + 3y + 1 = 0 and perpendicular to the line 7x + 4y - 10 = 0.
6.The base of a triangle is the line segment from (3,0) to (2,-3). If the area of the triangle is 7, find the general equation of the locus of the third vertex. (Two solutions).

Find the distance between the given lines:
a. 3x - y = 5 and 3x - y = 25
b. 4x - 6y = 9 and 2x - 3y = 6