SOLUTION: The standard form for the conic section is {{{(x+4)^2/3^2-(y+3/2)^2/(1/2)^2=1}}} What is the equation in general form? -------- The answer key I have shows x^2 - 36y^2

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The standard form for the conic section is {{{(x+4)^2/3^2-(y+3/2)^2/(1/2)^2=1}}} What is the equation in general form? -------- The answer key I have shows x^2 - 36y^2       Log On


   

Question 1204773: The standard form for the conic section is
%28x%2B4%29%5E2%2F3%5E2-%28y%2B3%2F2%29%5E2%2F%281%2F2%29%5E2=1
What is the equation in general form?
--------
The answer key I have shows x^2 - 36y^2 + 8x - 108y - 90 = 0
Could someone please show me how they worked out the solution step by step? My equation in general form differs in the last term.
Found 3 solutions by MathLover1, mananth, math_tutor2020:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B4%29%5E2%2F3%5E2-%28y%2B3%2F2%29%5E2%2F%281%2F2%29%5E2=1

%28x%2B4%29%5E2%2F9-%28y%2B3%2F2%29%5E2%2F%281%2F4%29=1

%28x%2B4%29%5E2%2F9-4%28y%2B3%2F2%29%5E2=1...both sides multiply by 9

%28x%2B4%29%5E2-36%28y%2B3%2F2%29%5E2=9

%28x%2B4%29%5E2-36%28y%5E2+%2B+3y+%2B+9%2F4%29=9

x%5E2+%2B+8x+-+36y%5E2+-+108y+-+65=9

x%5E2+%2B+8x+-+36y%5E2+-+108y+-+65-9=0

x%5E2+%2B+8x+-+36y%5E2+-+108y+-+74=0 =>The general form is this


not this x^2 - 36y^2 + 8x - 108y - 90 = 0

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
the answer key is wrong
The last term is -74
+x%5E2-36y%5E2%2B8x-108y-74=0
Just put this on any calculator and check



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

We can use a tool like Desmos to check to see if two conic section equations are the same or not.
https://www.desmos.com/calculator/ghu0cz1peh

In the 1st box is the original equation.
The 2nd box is the answer your textbook claims (unfortunately the wrong answer).
The 3rd box is the correct answer x^2 - 36y^2 + 8x - 108y - 74 = 0 where the 90 should be 74.


Curve1 and curve2 do not overlap, so we don't have a match.
But curve1 and curve3 do overlap.
Click on the 3rd graph to turn it on and off.
Repeatedly do this to have the curve blink different colors to help see the overlap.
Turn off curve2 if necessary.