Question 1188269: find the equation of the tangents and normal to curve x^2 - y^2 = 15, parallel to 4x - y + 20 = 0.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! find the equation of the tangents and normal to curve x^2 - y^2 = 15, parallel to 4x - y + 20 = 0.
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The slope of 4x - y + 20 = 0 is 4. m = 4
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Find the slope of the hyperbola.
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x^2 - y^2 = 15
2x*dx - 2y*dy = 0
dy/dx = x/y
---> x/y = 4 ---> y = x/4
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x^2 - y^2 = 15
x^2 - x^2/16 = 15
15x^2/16 = 15
15x^2 = 240
x^2 = 16, x = -4, +4
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At x = -4 and +4, y^2 = 1
---> the points (-4,-1) and (4,1)
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Use y - y1 = m*(x-x1) (m=4) to find the equations for the lines tangent.
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Use y - y1 = m*(x-x1) (m = -1/4) to find the equations for the lines normal.
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