parabola and rectangular hyperbola?
parabola y^2=4ax general point (at^2,2at) lies on parabola
the tangent to the parabola at point (ap^2,2ap) where p>0 and it passes through the point (-4a,0). find p
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parabola y^2=4ax general point (at^2,2at) lies on parabola
the tangent to the parabola at point (ap^2,2ap) where p>0 and it passes through the point (-4a,0). find p
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Verified answer
2y*y´=4a so y´= 4a/2y= 2a/2ap=1/p
so the tangent is
y-2ap=1/p(x-ap^2)
as it passes through (-4a,0)
-2ap= 1/p(-4a-ap^2) so
-2p= 1/p(-4-p^2) and -2p^2 = -4-p^2 so p^2 =4 and p=+-2