# Equations of Parallel and Perpendicular Lines - Page 19

Questions

- The width of a rectangle is 7 inches shorter than its length. The area is 78 square inches. What are the dimensions of the rectangle?
- If #AB# is defined by the endpoints #A(4,2)# and #B(8,6)#, what is the equation of the line that is the perpendicular bisector of #AB#?
- A square and a rectangle have the same perimeters. The length of a side of the square is #4x-1#. The length of the rectangle is #2x+1# and the width is #x+2#. How do you write and solve an equation to find #x#?
- The length of the table is #5# #m# greater than the width. The area is #84# #m^2#. What are the table dimensions?
- Find the intersection of perpendicular bisector of (a) line #k# joining #A(5,10)# and #B(-3,4)# and (b) line #l# joining #A(5,10)# and #C(-1,-2)#. Hence find the equation of circumcircle of #DeltaABC#?
- The normal at a point #P# of the ellipsoid #x^2/a^2+y^2/b^2+z^2/c^2=1# meets the coordinate planes in #A,B,C#. Show that #AP:BP:CP::a^2:b^2:c^2#?
- Angles from two given lines?
- Find the equation of the tangent planes to the conicoid #7x^2-3y^2-z^2+21=0#, which pass through the line #7x-6y+9=0, z=3#?
- What is the equation of the line perpendicular to y=3x-6 that runs through the point (-1,-3) ?
- How to find directions ratios of the line #(x-1)/2=(y+3)/1, z=2#?
- The length of a garden is #5# #m# longer than its width and the area is #14 m^2#. How long is the garden?
- Check if the line #x+1=1-y=-5z# lies on the plane #2x+3y-5z=1#?
- Prove that the planes #x+4y-3=1# and #-3x+6y+7z=0# are perpendicular to each other?
- Solve for the variables in each of the diagrams?
- The variable coefficient p,q,r in the equation of the straight line px+qy+r=0 are connected by the relation pa+qb+rc=0 where a,b and c are fixed contants.show that the variable line always passes through a fixed point?
- (at^2,2at) is a point on the line 2x-5y+12a=0,from this find the co-ordinates of two points on the line?
- Equation of perpendicular bisector and coordinates of a point on a line?
- If the length of perpendicular from origin to a line is #4# and line makes an intercept of #5# on #x#-axis, find its equation?
- Find the distance of point A(2,3) measured parallel to the line x- y = 5 from the line 2x + y + 6 = 0?