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Given the equation x2 − 14x + 2y2 + 45 = 0 find the foci, vertices, directrix, axis, and asymptotes, where app?

Given the equation x2 − 14x + 2y2 + 45 = 0

find the foci, vertices, directrix, axis, and asymptotes, where applicable.

Please, if anyone could go through how to get the right answer that would be awesome.

1 Answer

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  • ted s
    Lv 7
    7 years ago
    Favorite Answer

    this is an ellipse....[ x² - 14 x + 49] + 2y² = 4---> [ x - 7]² / 4 + y² / 2 = 1 { standard form }

    center ( 7 , 0 )...vertices of ( 7 ± 2 , 0 ) and ( 7 , 0 ± √2 )...axes x = 7 , y = 0..

    a² = b² + c² ---> c² = 2----> foci are ( 7 ± √2 , 0 )...directrices are x = 7 ± 2 √2

    now go to 'wikipedia.org ' , type in 'directrix of an ellipse'..and READ

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