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Psq is a Focal Chord of the Parabola Y2 = 8x. If Sp = 6, Then Write Sq. - Mathematics

PSQ is a focal chord of the parabola y2 = 8x. If SP = 6, then write SQ

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Solution

The coordinates of the focal chord are \[P \left( a t^2 , 2at \right) a\text{ and } Q \left( \frac{a}{t^2}, \frac{- 2a}{t} \right)\] 

Comparing y2 = 8x with

\[y^2 = 4ax\]
a = 2 
Therefore, the coordinates of the focus S is \[\left( 2, 0 \right)\] 
Given:
SP = 6 
\[\therefore \sqrt{\left( 2 - 2 t^2 \right)^2 + \left( 4t \right)^2} = 6\]
\[ \Rightarrow t^4 + 2 t^2 - 8 = 0\]
\[ \Rightarrow t^2 = 2\] 

Thus, we have:
SQ = \[\sqrt{\left( 2 - \frac{2}{t^2} \right)^2 + \left( \frac{4}{t^2} \right)}\] 

\[\sqrt{\left( 2 - \frac{2}{2} \right)^2 + \left( \frac{4}{2} \right)}\]

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 25 Parabola
Exercise 25.2 | Q 7 | Page 28
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