Question

The equation of the common normal to the parabola's y^2=4ax and x^2=4ay is

Answer 1

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MATHS

The equation of the common normal to the parabolas y

2

=4ax and x

2

=4ay is

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ANSWER

Equation of common normal to y

2

=4ax and x

2

=4ay is :

Equation of normal to y

2

=4ax is

y=mx−2am−am

3

.........(1)

x

2

=4a(mx−2am−am

3

)

x

2

−4amx+8a

2

m+4a

2

m

3

=0

Equal roots D=0

16a

2

m

2

−4(8a

2

m+4a

2

m

3

)=0

m

2

−m+2=0

m=2,−1

Put m=−1 in (1)

y=−x+2a+a

x+y=3a

Step-by-step explanation:

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