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12.1E: Ellipse (Mazoezi)

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    Kwa mazoezi yafuatayo, andika equation ya ellipse katika fomu ya kawaida. Kisha kutambua kituo, vertices, na foci.

    1. \(\frac{x^{2}}{25}+\frac{y^{2}}{64}=1\)

    2. \(\frac{(x-2)^{2}}{100}+\frac{(y+3)^{2}}{36}=1\)

    3. \(9 x^{2}+y^{2}+54 x-4 y+76=0\)

    4. \(9 x^{2}+36 y^{2}-36 x+72 y+36=0\)

    Kwa mazoezi yafuatayo, grafu ya ellipse, kituo cha kubainisha, vertices, na foci.

    5. \(\frac{x^{2}}{36}+\frac{y^{2}}{9}=1\)

    6. \(\frac{(x-4)^{2}}{25}+\frac{(y+3)^{2}}{49}=1\)

    7. \(4 x^{2}+y^{2}+16 x+4 y-44=0\)

    8. \(2 x^{2}+3 y^{2}-20 x+12 y+38=0\)

    Kwa mazoezi yafuatayo, tumia taarifa iliyotolewa ili kupata equation kwa duaradufu.

    9. Center katika (0,0), kuzingatia (3,0), kipeo katika (-5,0)

    10. Kituo cha\((2,-2),\) kipeo katika\((7,-2),\) lengo katika (4, -2)

    11. Nyumba ya sanaa ya whispering inapaswa kujengwa kama vile foci iko miguu 35 kutoka katikati. Ikiwa urefu wa nyumba ya sanaa ni kuwa miguu 100, urefu wa dari unapaswa kuwa nini?