Which rectangular equation corresponds to these parametric equations?

x = 0.2sec t and y = -0.25tan t

A) 25x^2 − 16y^2 = 1
B) 25x^2 + 16y^2 = 1
C) x^2 − 16y^2 = 25
D) 25y^2 − 16x^2 = 1
E) 4x^2 − 16x^2 = 1

since sec^2 = 1+tan^2,

(x/.2)^2 = (y/-.25)^2 + 1
25x^2 - 16y^2 = 1

Looks like A to me

To find the rectangular equation that corresponds to the given parametric equations, we can follow these steps:

Step 1: Express one of the parametric equations in terms of the other variable.
Since we have x in terms of t, we can rearrange the equation x = 0.2sec(t) to solve for sec(t) as follows:
sec(t) = x / 0.2

Step 2: Substitute the expression from step 1 into the other parametric equation.
Taking the second parametric equation y = -0.25tan(t), we can substitute the expression for sec(t) from step 1 to get:
y = -0.25tan(t) = -0.25 * (sin(t) / cos(t)) = -0.25 * (sin(t) / sqrt(1 - sin^2(t))) = -0.25 * (sqrt(1 - cos^2(t)) / cos(t)) = -0.25 * sqrt(1 - (x/0.2)^2) / (x/0.2)

Step 3: Simplify the expression obtained in step 2 to get the rectangular equation.
Multiplying both sides by (x/0.2) to eliminate the fraction, we have:
(x/0.2) * y = -0.25 * sqrt(1 - (x/0.2)^2)
xy/0.2 = -0.25 * sqrt(0.04 - x^2/0.04)
xy = -0.005 * sqrt(0.04 - x^2)

Therefore, the rectangular equation that corresponds to the given parametric equations is:
xy = -0.005 * sqrt(0.04 - x^2)

Among the given options, none of them matches the derived equation.