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Question: Classification of conic sections

Question:Classification of conic sections

janhardo 997
simplification conic
July 09 2020
0

I must do some formula manipulation
 

Classification of conic sections

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restart; with(student):
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A*x^2+B*y^2+C*x+D*y+E=0;

A*x^2+B*y^2+C*x+D*y+E = 0

 (1)
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f:= A*x^2+B*y^2+C*x+D*y+E;

A*x^2+B*y^2+C*x+D*y+E

 (2)
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completesquare(f, x);

A*(x+(1/2)*C/A)^2-(1/4)*C^2/A+B*y^2+D*y+E

 (3)
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f:= A*x^2+B*y^2+C*x+D*y+E;

A*x^2+B*y^2+C*x+D*y+E

 (4)
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ans:=Student[Precalculus][CompleteSquare]( (4), [y] );

B*(y+(1/2)*D/B)^2+A*x^2+C*x+E-(1/4)*D^2/B

 (5)
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ans1:=Student[Precalculus][CompleteSquare]( (4), [x] );

A*(x+(1/2)*C/A)^2-(1/4)*C^2/A+B*y^2+D*y+E

 (6)
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ans+ans1;

B*(y+(1/2)*D/B)^2+A*x^2+C*x+2*E-(1/4)*D^2/B+A*(x+(1/2)*C/A)^2-(1/4)*C^2/A+B*y^2+D*y

 (7)
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B*(y + D/(2*B))^2 + A*x^2 + C*x + 2*E - D^2/(4*B) + A*(x + C/(2*A))^2 - C^2/(4*A) + B*y^2 + D*y = 0;

B*(y+(1/2)*D/B)^2+A*x^2+C*x+2*E-(1/4)*D^2/B+A*(x+(1/2)*C/A)^2-(1/4)*C^2/A+B*y^2+D*y = 0

 (8)

Now i must  get this form A( )^2 +B( )^2 = M  

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Download vraag_herleiding_conic_sections_formule.mw

 

 
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