Question

3) Find a polar equation of the conic in terms of *r*
with its focus at the pole. ( r=???)

a)(4, *π*/2) (parabola)

b) (4, 0), (12, π) (eclipse)

c) (8,pi/2), (16,3pi/2) (eclipse)

Answer #1

1) Write a polar equation of a conic with the focus at
the origin and the given data: The curve is a hyperbola with
eccentricity 7/4 and directrix y=6.
2a) Determine the equation of a conic that satisfies
the given conditions:
vertices: (-1,2), (7,2)
foci: (-2,2), (8,2)
b) Identify the conic: circle parabola, ellipse,
hyperbola.
c) Sketch the conic.
d) If the conic is a hyperbola, determine the
equations of the asymptotes.

Write a polar equation of a conic with the focus at the origin
and the given data. hyperbola, eccentricity 5/3, directrix y =
4

The polar curve r = 5sin3θ where 0 ≤ θ ≤ π. Find the area of one
loop of the curve. Find an equation for the line tangent which has
a positive slope to the curve at the pole.

3)
a) Find a polar equation for the circle x^2 + (y -2)^2 = 4.
b)Find the arc length of the polar curve r =
3^θ from θ=0 to θ=2.

If r = 1 + sin(3θ) is the equation of a polar graph, find the
slope of the tangent line when θ = π

The Cartesian coordinates of a point are given. (a) (−3, 3)
(i) Find polar coordinates (r, θ) of the point, where r > 0
and 0 ≤ θ < 2π.
(r, θ) =
(ii) Find polar coordinates (r, θ) of the point, where r < 0
and 0 ≤ θ < 2π.
(r, θ) =
(b) (4, 4 sq root3 ) (i) Find polar coordinates (r, θ) of the
point, where r > 0 and 0 ≤ θ < 2π....

Find an equation for the conic section with the given
properties.
The ellipse with vertices V1(−3, −2) and V2(−3, 8) and foci
F1(−3, −1) and F2(−3, 7)

4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...

Find the area of one loop of the polar curve r=4*sin(3*theta +
Pi/3)
Let f(x,y) = 3x^2 + cos(Pi*y). a) f has a saddle point at (0,k)
whenever k is an odd integer b) f has a saddle point at (0,k)
whenever k is an even integer) c) f has a local maximum at (0,k)
whenever k is an even integer d) f has a local minimum at (0,k)
whenever k is an odd integer

verify that the polar coordinates (-4, pi/2) satisfies
the equation r=4sin3theta
and sketch a graph of the equation r=4sin3theta and locate the
point from above and approximate the location of any vertical
tangent lines

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