Tutorial Equations of Tangent and Normal to a Parabola


Equations of Tangent and Normal to a Parabola


   


Here we list the equation of tangent and normal for different forms of parabola:


1. Equation of tangent to the parabola y^(2)=4ax at (x_1,y_1)is yy_1=2a(x x_1).
2. Equation of normal to the parabola y^(2)=4ax at (x_1,y_1)is y-y_1=-(y_1)/(2a)(x x_1).
3. If -(y_1)/(2a)=m then equation of normal line is y=mx-2am-am^(3).
4. The line y=mx c touches the parabola y^(2)=4ax if c=(a)/(m).
5. Equation of tangent to the parabola y^(2)=4ax at (at^(2),2at)is x-ty at^(2)=0.
6. Equation of normal to the parabola y^(2)=4ax at (at^(2),2at)is y tx=2at at^(3).




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