InterviewSolution
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InterviewSolution
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The line `lx+my+n=0` is a normal to the parabola `y^2 = 4ax` ifA. `mn = al ^ 2 `B. ` lm = an ^ 2 `C. `ln = am ^ 2 `D. None of the above |
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Answer» Correct Answer - C Given ,parabola, ` y ^ 2 = 4 ax ` ` rArr 2y ( dy ) /( dx ) = 4a ` ` rArr ( d y ) /( dx ) = (2a ) /( y ) " " ` … (i) which is the slope of tangent Given ` lx + my + n = 0 ` is an equation of tangent of the parabola `y^ 2 =4a x ` ` therefore ` Slope of tangent ` = - ( 1 ) /( m ) " "` ... (ii) From Eqs (i) and (ii) ` (2a )/( y ) = - ( l ) / ( m ) rArr y = ( - 2am ) /( l ) ` ` because y ^ 2 = 4ax ` ` rArr ( 4a ^ 2 m^ 2 ) /( l ^ 2 ) = 4ax` ` rArr x = ( am^ 2 ) /( l^ 2 ) ` On putting the values of x and y in the following equation ` l ( ( am^2 ) /( l^2 )) +m ( ( -2 am ) /( l ) ) + n = 0` ` ( am ^ 2 ) /( l ) -(2am ^ 2 ) /( l) + n = 0 ` ` rArr ( am^ 2 ) / ( l) = n rArr am ^ 2 = n l` Which is the required relation. |
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