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Maths-

General

Easy

Question

Straight line $ell$ x + my + n = 0 touches parabola y² = 4ax if $ell$ n = am^k then k =

1
2
3
$\frac{3}{2}$

The correct answer is: 2

To find the value of k.
The x-coordinates of the points of intersection of the line $l x + m y + n = 0$ and parabola is
$open parentheses negative fraction numerator l x plus n over denominator n end fraction close parentheses squared equals 4 a x l squared x squared plus 2 x left parenthesis ln minus 2 a m squared right parenthesis plus n squared equals 0 I f space t h e space l i n e space l x plus m y plus n equals 0 space t o u c h e s space t h e space p a r a b o l a comma space t h e n space t h i s space e q u a t i o n space h a s space e q u a l space r o o t s 4 left parenthesis ln minus 2 a m squared right parenthesis squared minus 4 l to the power of 2 end exponent n to the power of 2 end exponent equals 0 minus 4 a l m squared n plus 4 a squared m to the power of 4 equals 0 ln equals a m squared$

Therefore, the value of k is 2.

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