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Hyperbola : intersection of asymptotes?
Find the co - ordinates of the two points Q and R , where the tangent to the hyperbola x^2/45 - y^2/20 = 1 at the point (9,4) intersects the two asymptotes
1 Answer
- Ed ILv 71 decade agoFavorite Answer
x^2/45 - y^2/20 = 1
2x/45 - 2y/20 dy/dx = 0
-2y/20 dy/dx = -2x/45
dy/dx = 4x/(9y)
At (9, 4), the slope is 1.
y - 4 = 1(x - 9)
y - 4 = x - 9
-x + y = -5
y = x - 5 is the equation of the tangent line.
x^2/45 - (x - 5)^2/20 = 0 are the equations of the asymptotes.
x^2/45 - (x^2 - 10x + 25)/20 = 0
20x^2 - 45x^2 + 450x - 1125 = 0
-25x^2 + 450x - 1125 = 0
x^2 - 18x + 45 = 0
(x - 15)(x - 3) = 0
x = 15 or x = 3
y = 10 or y = -2
Q(15, 10)
R(3, -2)
