Please help me set up these problems.

1.) Find an equivalent equation in rectangular coordinates.
r(1 - 2 cos θ) = 1

2.) Find a rectangular equation for the plane curve defined by the parametric equations.
x = sec t, y = tan

3.) A projectile is fired with an initial velocity of 500 feet per second at an angle of 70° with the horizontal. To the nearest 10 feet, find the horizontal distance covered by the projectile.

1 answer

Review the equation for a hyperbola in polar coordinates.

#2 Hint: sec^2 = 1 + tan^2

#3
y = 500 sin70° t - 16t^2
Solve for t when y=0 to find the time in flight

The x-velocity is constant at 700 cos70°

So using the time from step 1, distance = speed * time