Matematika

Pertanyaan

salah satu persamaan garis singgung lingakaran x² + y² + 4x + 2y - 20 = 0 yang sejajar garis 3x +4y = 7

1 Jawaban

  • x² + y² + 4x + 2y - 20 = 0
    (x+2)² + 4 + (y+1)² +1 -20 = 0
    (x+2)² + (y+1)² = 20-4-1
    (x+2)² + (y+1)² = 15

    m = -x/y = -3/4
    r² = 15
    r = √15
    y-y1 = m(x-x1) ± r√1+m²
    y+1 = -3/4(x+2) ± √15√1+(-3/4)²
    y+1 = -3/4x - 3/2 ± √15√1+(9/16)
    y+1 = -3/4x - 3/2 ± √15.√25/16
    y+1 = -3/4x -3/2 ± √15(5/4)
    4y + 4 = -3x -6 ± 5√15

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