InterviewSolution
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InterviewSolution
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If and k are segments of a focal chord of the parabola `y^(2)= 4ax`, then k =A. ` ( ab ) /( a- b ) `B. ` ( a ) /( b - a ) `C. ` ( b ) /( b - a ) `D. ` ( ab ) /( b - a ) ` |
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Answer» Correct Answer - D For latusrectum PQ, ` y ( t _ 1 + t _ 2 ) - 2x - 2a t _ 1 t _ 2 = 0 ` and ` t _ 1 t _ 2 = - 1 ` For any point ` P ( x , y ) `, then focal distance is ` a + x `. ` therefore b = a + x = a + a t _ 1 ^ 2 = a ( 1 + t _ 1 ^ 2 ) ` ...(i ) ` c = a + x = a + at _ 2 ^ 2 = a + ( a ) /( t _ 1 ^ 2 ) ( because t _ 1 t _ 2 = - 1 ) ` ` = ( a ( 1 + t _ 1 ^ 2 ) ) /( t _ 1^ 2) " " `... (ii) ` therefore (b )/ (c ) = t _ 1 ^ 2 ` ` therefore ` From Eq. (i), ` b = a ( 1 + (b)/ (c )) ` ` rArr b = a + ( ab ) / ( c ) ` ` therefore c = ( ab ) /( b - a ) ` |
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