Answer the following questions....

1) Rewrite the equation in a rotated x'y'-system without an x'y' term. Express the equation involving x' and y' in the standard form of a conic section. x²+ xy + y²- 3y - 6 = 0

2) Write the equation in terms of a rotated x'y'-system using , the angle of rotation. Write the equation involving x' and y' in standard form. 14x²+ 12xy + 2y²- 17 = 0; = 30

3) An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 16 inches tall and stand 80 inches apart. Find the vertical distance from the roadway to the cable at a point on the road 12 inches from the lowest point of the cable.