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  • The locus of the middle points of chords of the parabola drawn through the vertex i

The locus of the middle points of chords of the parabola \mathrm{y^2=8 x} drawn through the vertex is a parabola whose
 

Option: 1

 focus is (2,0)
 


Option: 2

 latus rectum =8
 


Option: 3

 focus is (0,2)
 


Option: 4

 latus rectum =4
 


Answers (1)

best_answer

If the middle point of a chord is  (\alpha, \beta), then \mathrm{ \alpha=\frac{2 t^2+0}{2}, \beta=\frac{4 t+0}{2}}

Elininating \mathrm{t,} \mathrm{\alpha=\left(\frac{\beta}{2}\right)^2}

So, the locus is \mathrm{y^2=4 x}

Posted by

Gautam harsolia

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