Question

What is the equation of tangent to the parabola y2 =4ax at the point (x,y)

Answer 1

Answer: The equation of tangent to the parabola y^2 =4ax at a point (x',y') is yy' =2ax +2ax'

Explanation:

• Differentiating the equation of the parabola, we will get the slope of tangent at any point as

dy/dx = 2a/y

• Slope of tangent at point (x',y') = 2a/y'

• The equation of line passing through point (x',y') having slope 2a/y' is

yy'-y'^2 = 2ax -2ax'.......... eq.(1)

• This point (x',y') also lies on the parabola so, it must satisfy equation of parabola.

y'^2 = 4ax'.......eq.(2)

• Substitute eq.(2) in eq.(1)

• yy' - 4ax' = 2ax - 2ax'

The simplified form of the above equation of the tangent is

yy' = 2ax + 2ax' which is our required answer.