Date: Fri, 6 Aug 1999 03:34:24 -0600 (CST)
Subject: parametric equation

Name: Nicholas
Who is asking: Student

Show that an equation of the normal to the curve with parametric equations x=ct y=c/t t not equal to 0, at the point (cp, c/p) is :


Hi Nicholas,

The slope of the normal to a curve at a point P is -1 divided by the slope of the tangent to the curve at P, and the slope of the tangent to the curve at P is given by the derivative dy/dx at P. Your curve is given in terms of a parameter t and thus you can calculate dy/dx by:

Using x=ct and y=c/t find dy/dt and dx/dt and then use the expression above to find dy/dx at the point P(cp,c/p). Use the result to calculate the slope of the normal at P and then write the equation of the line with this slope that passes through P.



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