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  • The locus of mid–point of family of chords (parameter) of the parabola

The locus of mid–point of family of chords \lambda x+y-5=0 (parameter) of the parabola
x^2=20 y is

Option: 1

y^2=10(x-5)


Option: 2

x^2=10(y-5)


Option: 3

x^2+y^2=25


Option: 4

 none of these


Answers (1)

best_answer

\lambda x+y-5=0 is the focal chord 

Since it passes through (0, 5) 

Let h, k be the mid point of all such chord 

h=5\left(t_1+t_2\right), k=5\left(\frac{t_1^2+t_2^2}{2}\right)_{\left(t_1 t_2-1\right)}

On eliminating t_1, t_2

\mathrm{x}^2=10(\mathrm{y}-5)

 

Posted by

vinayak

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