Question

5. Find the value of a if the straight lines 5x-2y-9=0 and ay + 2x -11 = 0 are
perpendicular to each other.

Answer 1

Solution:-

given by:-
straight lines 5x-2y-9=0 and ay + 2x -11 = 0 are
perpendicular to each other.

we have :-
$5x - 2y - 9 = 0 \\ slope \: (m1) = \frac{ - 5}{ - 2} = \frac{5}{2} \\ ay + 2x - 11 = 0 \\ 2x + ay - 11 = 0 \\ slope \: (m2) = \frac{ - 2}{ a}$
here

both are pependicular

then ,

》 (m1)×(m2) = -1

》 = 5/2 × (-2/a) = -1

》 = -5/a = -1

》=( a = 5) ans

☆i hope its help☆

Answer 2

Solution :

i ) Compare 5x - 2y - 9 = 0 with

ax + by + c = 0 , we get

a = 5 , b = -2 , c = -9

slope of a line ( m1 ) = -a/b

=> m1 = - 5/( -2 )

=> m1 = 5/2 ------( 1 )

ii ) Slope of a line ay + 2x - 11 = 0

=> 2x + ay - 11 = 0

slope ( m2 ) = - 2/a ---( 2 )

according to the problem given ,

m1 × m2 = -1

=> 5/2 × ( -2/a ) = -1

=> 5/a = 1

=> 5 = a

Therefore ,

a = 5

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