What is the equation of chord joining 2 points of a parabola given by parameters t1 and t2-A- 2 x-t1-t2 y-2 t1 t2-0B- 2 y-t1-t2 x-t1 t2-0C- 2 x-t1-t2 y-2 a t1 t2-0D- 2 y-t1-t2 x-2 t1 t2-0

The correct option is C the parameters of the 2 joining points are t_1 and t_2 i.e.,A≡(at_1^2,2at_1) B≡(at_1^2,2at_2) ∴ AB is given by (y 2at_1)=2a(t_1 t_2)/ ...

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Standard XI

Mathematics

Terminologies Related to a Hyperbola

What is the e...

Question

What is the equation of chord joining 2 points of a parabola given by parameters $t_{1} a n d t_{2}$ .

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Solution

The correct option is C

the parameters of the 2 joining points are $t_{1} a n d t_{2}$

i.e., $A \equiv (a t_{1}^{2}, 2 a t_{1})$

$B \equiv (a t_{1}^{2}, 2 a t_{2})$

$∴$ AB is given by

$(y - 2 a t_{1}) = \frac{2 a (t_{1} - t_{2})}{a (t_{1}^{2} - t_{2}^{2})} . (x - a t_{1}^{2})$

$(y - 2 a t_{1}) = [\frac{2}{t_{1} + t_{2}}] (x - a t_{1}^{2})$

$y (t_{1} + t_{2}) - 2 a t_{1}^{2} - 2 a t_{1} t_{2} = 2 x - 2 a t_{1}^{2}$

i.e., $2 x - (t_{1} + t_{2}) y - 2 a t_{1} t_{2} = 0$ _{is the required equation of the chord. This would be a useful formula is you could remember in higher level problems involving chord of a parabola.}

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What is the equation of chord joining 2 points of a parabola given by parameters t1 and t2.

What is the equation of chord joining 2 points of a parabola given by parameters $t_{1} a n d t_{2}$ .