Find the coordinates and foci of the conic : 4(x+2)2 = 36-9(y-1)2Find the equations of the asymptotes for the conic: 25x2-150x-16y2-64y-239=0Find the equation of an ellipse with a focus at (-5,2) and vertices at (-5,-1) and (-5,6)Find the area inside the conic x2+6x=4y-y2Find the parametric equations of a circle centered at (5,6) with a radius of 4 and where the particle moves in a clockwise direction starting at (5,10) around the circle in 60 seconds. Use parameter 't' as time (in  seconds)Eliminate the parameter and find the corresponding rectangular equation for the set of parametric equations; find the coordinates of the focus of the resulting curve x=3-t2 & y = t+2

Question
Asked May 6, 2019
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  1. Find the coordinates and foci of the conic : 4(x+2)2 = 36-9(y-1)2
  2. Find the equations of the asymptotes for the conic: 25x2-150x-16y2-64y-239=0
  3. Find the equation of an ellipse with a focus at (-5,2) and vertices at (-5,-1) and (-5,6)
  4. Find the area inside the conic x2+6x=4y-y2
  5. Find the parametric equations of a circle centered at (5,6) with a radius of 4 and where the particle moves in a clockwise direction starting at (5,10) around the circle in 60 seconds. Use parameter 't' as time (in  seconds)
  6. Eliminate the parameter and find the corresponding rectangular equation for the set of parametric equations; find the coordinates of the focus of the resulting curve x=3-t2 & y = t+2 
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Expert Answer

Step 1

Given information:

The given conic equation is 4(x+2)2 = 36-9(y-1)2.

Calculation:

First, rewrite the given equation, we get

 

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Step 2

Now, divide by 36 on  both sides of the equation, we get

 

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Step 3

The general equation ...

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