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Maths-

General

Easy

Question

If line 2x + y + λ = 0 is normal to y² = 8x than λ =

24
– 24
– 8
None

The correct answer is: – 24

To find the value of λ.
$y squared equals 4 a x 2 y fraction numerator d y over denominator d x end fraction equals 8 fraction numerator d y over denominator d x end fraction equals 4 over y s l o p e space o f n o r m a l space o f space p a r a b o l a equals fraction numerator negative y over denominator 4 end fraction G i v e n comma space 2 x plus y plus lambda equals 0 space i s space a space e q u a t i o n space o f space n o r m a l space o f space t h e space p a r a b o l a space y space space 2 space space equals 8 x. S l o p e space o f space n o r m a l space equals negative 2 equals fraction numerator negative y over denominator 4 end fraction y equals 8 f r o m space p a r a b o l i c space e q u a t i o n comma space x equals 8 p u t t i n g space t h e space v a l u e s space o f space space x space a n d space y space i n space t h e space e q u a t i o n space o f space n o r m a l space 2 left parenthesis 8 right parenthesis plus 8 plus lambda equals 0 space rightwards double arrow lambda equals negative 24$

Therefore, the value of $λ is -24.$

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