Hi, I'll be grateful if you could help with this problem. The tangents of the parabola x2 - mx + 3/2 intersect perpendicularly at the origin, then what is the positive value of m? Thanks in advance.
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Hi The equation of the tangent at the point whose abscissa is "a" is y = (2a-m)x-a²+3/2 The tangent passes through the origin when -a²+3/2 = 0 This gives 2 values : a1=sqrt(3/2) and a2=-sqrt(3/2) Spoiler: The two tangent intersect perpendicularly when (2a1-m)(2a2-m)=-1 m²-2(a1+a2)m+4a1a2=-1 m²-5=0 m=+/-sqrt(5)
Thank you! You helped a lot!
Last edited by truevein; June 6th 2010 at 01:00 PM.
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