Find an equation in x and y for the conic section with polar equation r=1/1+cos

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We have the polar identities:

x = r cos(q)
y = r sin ...

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A polar equation is written in x,y form. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Equation Point
4x^2-24x-25y^2+250y-489=0 (27⁄4,5⁄2)
( 1) identify the conicsection represented by the equation.
( 2) write the equation of the conicsection in standard form.
( 3) identify all relevant key elements of

Please see the attached file for the fully formatted problems.
1. Solve the system of equations algebraically. Be sure to find all
solutions!
X^2+y^2=10
2x^2-y^2=17
I got not sure if it's right or missing
x=2.999999976132
Y=0.999999870315
2. Find the coefficient of the term x^5 y^3 in the expansion of (4x

Graph an ellipse as a polar function with a focus at the pole and parameterized by the eccentricity e and the distance d
between the focus and a vertical directrix.
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Please show me how step-by-step on how you would graph this.
Thanks

Please see the attached file for the fully formatted problems.
8. Let a function f (z) = u + i v be differentiable at a nonzero point z0 = r0 e(iθ0). Use the expressions for ux and vx found in Exercise 7, together with the polar form (6) of Cauchy-Riemann equations, to rewrite the expression
f ΄(z0) = ux + i vx

Please assist with the attached problem.
(a) Calculate the Laplacian of function u(x,y,z) = x^3 - 3xy^2 + z^2 in 3D Cartesian coordinates.
(b) Convert the formula for u into formula for u involving cylindrical polar coordinates. Then compute the Laplacian using the cylindrical polar form. Show that your answer here is the same

Using first two equations determine 3 possible points that the 2 conicsections that you get from equations meet. Add a third equation figure to out the one point that all three conicsections meet.
First equation is 9(x-squared)+25(y-squared)-72x=81
Second equation is 9(x-squared)-15(y-squared)=9
Graph these two conical