1. The points (1,3) and (5,1) are the opposite vertices of a rectangle. The other two vertices are on the line y=2x+c. Find c and the remaining vertices.
2. The consecutive sides of a parallelogram are 4x+5y=0 and 7x+2y=0. If the equation of one diagonal be 11x+7y=9, find the equation of the other diagonal.
3. One side of a rectangle lies along the line 4x+7y+5=0. Two of its vertices are (-3,1) and (1,1). Find the equations of the other three sides.
4. Find the equations of straight lines passing through (-2, -7) and having an intercept of length 3 between the straight lines 4x+3y=12 and 4x+3y=3.
5. Find the equation of the circle which passes through the point (2,0) and whose centre is the limit of the point of intersection of the lines 3x+5y=1 and (2+c)x+5c²y=1 as c tends to 1.
6. Two vertices of a triangle are (6,4) and (2,6). If the centroid of the triangle is (4,6), find the coordinates of the third vertex.
7. Find the circumcentre of the triangle whose vertices are (1,1), (2, -1) and (3,2).
8. Find the value of k such that the three points (k,2k), (2k,3k) and (3,1) are collinear.
9. Find the area of the quadrilateral whose vertices are (-1,-5),
(2,-3), (1,2), and (-2, 4).
10. Find the equations of the circles passing through (-4,3) and touching the lines x+y=2 and x-y=2.