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The asymptotes of a hyperbola are y=x+1 and y=3-x. Also, the hyperbola passes through (3,3). Find the distance between the foci of the hyperbola.

 Mar 27, 2019
 #1
avatar+12530 
+1

The asymptotes of a hyperbola are y=x+1 and y=3-x. Also, the hyperbola passes through (3,3). Find the distance between the foci of the hyperbola.

laugh

 Mar 27, 2019
edited by Omi67  Mar 27, 2019
 #2
avatar+26397 
+2

The asymptotes of a hyperbola are y=x+1 and y=3-x. Also, the hyperbola passes through (3,3).
Find the distance between the foci of the hyperbola.

 

Formula hyperbola:

1. asymptotex+1=yx+1y=02. asymptote3x=y3xy=0hyperbola: (x+1y)(3xy)+c=0P(x=3,y=3)(3+13)(333)+c=0(1)(3)+c=0c=3hyperbola: (x+1y)(3xy)+3=0(x+1y)(3xy)+3=0((xy)+1)(3(x+y))+3=03(xy)(xy)(x+y)+3(x+y)+3=03(xy)(xy)(x+y)+3(x+y)+3=03x3y(x2y2)+3xy+3=02x4yx2+y2+6=0|(1)x22xy2+4y6=0x22xy2+4y=6(x1)21(y2)2+4=6(x1)2(y2)2=3|:3(x1)23(y2)23=1Formula hyperbola:(xh)2a2(xk)2b2=1a2=3a=3b2=3b=3

 

Focus1:F1(h+ae,k)Focus2:F2(hae,k)Foci distance:h+ae(hae)=h+aeh+ae=2ae|e=a2+b2a=2aa2+b2a=2a2+b2|a2=b2=3=23+3=26

 

The distance between the foci of the hyperbola is 26

 

 

laugh

 Mar 27, 2019
edited by heureka  Mar 27, 2019

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