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Identifikasi irisan kerucut $$$x^{2} \ln\left(4\right) \ln\left(43\right) = \ln\left(415\right)$$$
Kalkulator terkait: Kalkulator Parabola, Kalkulator Lingkaran, Kalkulator Elips, Kalkulator Hiperbola
Masukan Anda
Identifikasi dan temukan sifat-sifat irisan kerucut $$$x^{2} \ln\left(4\right) \ln\left(43\right) = \ln\left(415\right)$$$.
Solusi
Persamaan umum suatu irisan kerucut adalah $$$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$$$.
Dalam kasus kita, $$$A = \ln\left(4\right) \ln\left(43\right)$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = 0$$$, $$$E = 0$$$, $$$F = - \ln\left(415\right)$$$.
Diskriminan irisan kerucut adalah $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = 0$$$.
Selanjutnya, $$$B^{2} - 4 A C = 0$$$.
Karena $$$\Delta = 0$$$, ini adalah irisan kerucut degenerat.
Karena $$$B^{2} - 4 A C = 0$$$, persamaan tersebut menyatakan dua garis sejajar.
Jawaban
$$$x^{2} \ln\left(4\right) \ln\left(43\right) = \ln\left(415\right)$$$A menyatakan sepasang garis $$$x = - \frac{\sqrt{\ln\left(256\right)} \sqrt{\ln\left(415\right)}}{2 \ln\left(4\right) \sqrt{\ln\left(43\right)}}$$$, $$$x = \frac{\sqrt{\ln\left(256\right)} \sqrt{\ln\left(415\right)}}{2 \ln\left(4\right) \sqrt{\ln\left(43\right)}}$$$A.
Bentuk umum: $$$x^{2} \ln\left(4\right) \ln\left(43\right) - \ln\left(415\right) = 0$$$A.
Bentuk terfaktorkan: $$$\left(2 x \ln\left(4\right) \sqrt{\ln\left(43\right)} - \sqrt{\ln\left(256\right)} \sqrt{\ln\left(415\right)}\right) \left(2 x \ln\left(4\right) \sqrt{\ln\left(43\right)} + \sqrt{\ln\left(256\right)} \sqrt{\ln\left(415\right)}\right) = 0.$$$A
Grafik: lihat kalkulator grafik.