Find and calculate the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections x^2 + 2y^2 - 2x - 4y = -1

Ramsey 2020-11-12 Answered
Find and calculate the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections x2+2y22x4y=1
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Expert Answer

berggansS
Answered 2020-11-13 Author has 91 answers
Given x2+2y22x4y=1
(x22x)+2(y22y)=1
(x22x+1)+2(y22y+1)=1+1+2
(x1)2+2(y1)2=2
(x1)22+2(y1)22=22
(x1)22+(y1)2=1 It is in the form of (xh)2a2+(yk)2b2=1
a2=2,b2=1
a=2,b=1 Distance between center and focus c=21
=1 Hence Center(h,k)=(1,1) Foci =(h±c,k)
=(1±1,1) Vertices =(h±a,k)
=(1±2,1)
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