Eliminate the parameter t Then use the rectangular equation

Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the giver parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x = 4 sec t, y = 6 tan t: -infinity

Solution

ANS: Here x/4 = sec t and y/6 = tan t.

We know that 1 + (tan t)^2 = (sec t)^2 >> (sec t)^2 - (tan t)^2 = 1.

Here, (x/4)^2 - (y/6)^2 = 1 (x^2)/16 - (y^2)/36 = 1 which is option a.

The graph will have vertices at (4,0) & (-4,0) and the center at (0,0) .

The image of the graph isn\'t clear but I think it is the 2nd from the left.