Question

Find the equation of tangent to parabola
y²=4ax at the extremities of its latus rectum

Answer 1

Answer:

The equation of tangent to parabola

y²=4ax at the extremities of its latus rectum is,

y− (−2a) = 1(x−a)

           y = x−a−2a

           y = x−3a

Step-by-step explanation:

From the above question,

Let the parabola be y2=4ax and extremities of latus

rectum are (a,2a) & (a,-2a)

P is the point of intersection of two tangents

Equation of tangent at A

           yy1=2a(x+x1)

           y(2a)=2a(x+a)

           y=x+a

Equation of tangent at B

           y(−2a)=2a(x+a)

           y=−x−a

Now, we shall calculate the equation of normal at point A

Equation of normal at point A

           y−2a=−1(x−a)

           y=−x+a+2a

           y=−x+3a

Slope of normal at through point B

Equation of normal at point B

           y−(−2a)=1(x−a)

           y=x−a−2a

           y=x−3a

Hence the equation of tangent to parabola

y²=4ax at the extremities of its latus rectum is  y=x−3a

For more related question : https://brainly.in/question/6937613

#SPJ1