Eliminate the parameter and obtain the standard form of the rectangular equation. hyperbola: x = h + b tan(θ), y = k + a sec(θ) use your result to find a set of parametric equations for the line or conic. (when 0 ≤ θ ≤ 2π. set your center at the origin. enter your answers as a comma-separated list of equations.) hyperbola: vertices: (0, ±2); foci: (0, ± 5 )

Problem 1:

Problem 2:

Step-by-step explanation:

I'm going to make a guess here.

That this is two problems.

Problem 1:

Eliminate the parameter in

and

.

Recall the following Pythagorean Identity:

If we solve our first equation: for the tangent piece we can substitute into this identity.  We will also need to solve for the secant piece in .

Let's do the equation for x first:

Subtract h on both sides:

Divide both sides by b:

.

Let's now look at the equation for y:

Subtract k on both sides:

Divide boht sides by a:

.

Now we are going to substitute this into our identity:

We are going to subtract the tangent squared piece on both sides to get 1 by itself:

This an equation for an hyperbola with center .

The vertices are at .

The foci is at where .

Problem 2:

We want the equation parametric equations for the conic given:

Hyperbola with vertices and foci and center at (0,0).

We are using the information from the first sentence.

We have (h,k)=(0,0).

We have a=2 and c=5 so we need to find b.

Subtract 4 on both sides:

Square root both sides:

Let's put into our formula for the parametric equations now:

.

We don't really need that 0 in there:

h df tyjgtyj ttd y ytkgfty ty

step-by-step explanation:

tyty jry j y yj yttj yhgtyj y ghyj ytthj

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this