Question

A parabola is given by y²=2px and passes through A(4/7,-4). What is the equation of a tangent line to the parabola through the point A?

Answer 1

Given :  A parabola is given by y²=2px and passes through A(4/7,-4).

To Find :  the equation of a tangent line to the parabola through the point A

Solution:

y²=2px

passes through A(4/7,-4).

=> (-4)²  = 2 p ( 4/7)

=> 16  = 8p/7

=> 2 = p/7

=> p = 14

y²=2px

=> y²  = 28x

2ydy/dx =  28

=>dy/dx  = 28/2y

=> dy/dx  = 14/y

A(4/7,-4)

=> m = 14/(-4)   =  -  7/2

y - (-4)  = (-7/2) (x  -  4/7)

=> y + 4  = -7x/2  + 2

=> 2y + 8  = -7x  + 4

=> 7x + 2y  + 4 = 0

7x + 2y  + 4 = 0  is the equation of a tangent line to the parabola through the point A

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