document.write( "Question 1188269: find the equation of the tangents and normal to curve x^2 - y^2 = 15, parallel to 4x - y + 20 = 0. \n" ); document.write( "

Algebra.Com's Answer #819317 by Alan3354(69443) $\"\"$ $\"About$

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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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\n" ); document.write( "The slope of 4x - y + 20 = 0 is 4. m = 4
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\n" ); document.write( "Find the slope of the hyperbola.
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\n" ); document.write( "x^2 - y^2 = 15
\n" ); document.write( "2x*dx - 2y*dy = 0
\n" ); document.write( "dy/dx = x/y
\n" ); document.write( "---> x/y = 4 ---> y = x/4
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\n" ); document.write( "x^2 - y^2 = 15
\n" ); document.write( "x^2 - x^2/16 = 15
\n" ); document.write( "15x^2/16 = 15
\n" ); document.write( "15x^2 = 240
\n" ); document.write( "x^2 = 16, x = -4, +4
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\n" ); document.write( "At x = -4 and +4, y^2 = 1
\n" ); document.write( "---> the points (-4,-1) and (4,1)
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\n" ); document.write( "Use y - y1 = m*(x-x1) (m=4) to find the equations for the lines tangent.
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\n" ); document.write( "Use y - y1 = m*(x-x1) (m = -1/4) to find the equations for the lines normal.
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