Write the general equation of ellipse with the center at the origin, foci have coordinates 0,4 and 0, -4 and one of the vertex is at  0, -5?

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  • 1 month ago

    you have a vertical ellipse.... F1( 0, -4 )   F2( 0, 4 )   V1( 0, - 5) 

    eqn:   ( x - h )^2  / b^2  +  ( y - k )^2 / a^2  = 1

                       and         

            c^2 =  a^2 - b^2  

        

      h = k = 0  since  center is  origin

    so  a = 5  since vertex  is  5 units away from the center,    and  foci are  4 units from center, so  c = 4           length of  ellipse is  2a

    what is  b^2 ?      b  represents  the  " 1/2 width"  from the center  left, right of the center.

    [   width  would  be  2b  .......  2b or not 2b, that is the question .... ?   sorry, couldn't resist :)  ]

    4^2 = 5^2 - b^2         I'll let  you solve for  b^2

    you have it all... a,  so calculate a^2 ,   b^2   h,k = 0 in this problem, and put them into your equation.

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