#$&*
mth 164
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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With an equation like y = 7x^2, I do not understand how to write it in polar form. All of the problems that I have worked that are in polar form look like z= x + yi. They all have an i in the problem or addition. How would I work this with no i and no addition..with an exponent. I know that polar form is z= x + yi= (r cos theta) + (r sin theta)i = r (cos theta + i sin theta)I do not understand how to set up the problem with out those things.
@& z = x + y `i is the complex-number form of the point (x, y) in the plane.
The polar coordinates of the point (x, y) are r and theta, where r = sqrt(x^2 + y^2) and theta = arcTan(y / x), plus 180 degrees if x < 0.
x = r cos(ttheta) and y = r sin(theta)
y = 7 x^2
could be written
r sin(theta) = 7 ( r cos(theta))^2
which expands to
r sin(theta) = 7 r^2 cos^2(theta)
Solving for r we have
r = 1/7 * sin(theta) / cos^2(theta)
or
r = 1/7 * tan(theta) sec(theta)*@
Also, with other problems, where it says for example to Find the equation of an ellipse centered at ( 6, 7) with major axis of length 5 parallel to the y axis. I do not understand how to set this up or work it either with out knowing the vetex or foci. I couldnt find any examples in the book of these two types.
@& The standard equation of an ellipse centered at point (h, k) with semi-axes a in the x direction and b in the y direction is
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1.
Knowing the coordinates of the center you have h and k.
Knowing that the major axis is parallel to the y axis and has length 5, you know that the semimajor axis is parallel to the y axis and has length 2.5. So b = 2.5.
The information you quote isn't sufficient to find a. If you were given the minor or semi-minor axis you would be able to find a. If you were given a point (x, y) on the ellipse you could substitute this into the equation, along with your known values of h, k and b and solve for a.*@
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@& See if my notes help. Additional questions are welcome.*@