Matematika

Pertanyaan

persamaan garis singgung lingkaran x2 + y2 - 6x + 10y - 91 = 0 yang melalui titik (-7, -10) adalah...

1 Jawaban

  • a = (-1/2) × (-6) = 3
    b = (-1/2) × (10) = -5
    r = √(a² + b² - C)
    = √(3² + (-5)² - (-91))
    = √(9+25+91)
    = √(125)
    r² = 125

    (X-a)(X1-a) + (Y-b)(Y1-b) = r²
    (X-3)(-7-3) + (Y+5)(-10+5) = 125
    (X-3)(-10) + (Y+5)(-5) = 125
    -10X + 30 - 5Y - 25 = 125
    -10X - 5Y +5 = 125
    -10X - 5Y = 120 (Bagi -5)
    2X + Y = -24
    2X + Y + 24 = 0

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