Question

4. If the straight lines y/2=x-p and ax+5 =3y are parallel, then find a.

Answer 1

solution:-

given by:-
the straight lines y/2=x-p and ax+5 =3y are parallel.

we have:-

$\frac{y}{2} = x - p \\ y = 2x - 2p \\ 2x - y - 2p = 0 \\ slope(m1) = \frac{ - 2}{ - 1} = 2 \\ ax + 5 = 3y \\ ax - 3y + 5 = 0 \\ slope \:( m2) = \frac{ - a}{ - 3} = \frac{a}{3} \\ here \:$

》both lines are parallel
》then ,
》 m(1) = (m2)

》 2 = a/3

( a = 6) ans


☆ i hope its help☆

Answer 2

Solution :

i ) Given y/2 = x - p

=> x - y/2 - p = 0 Compare this with

ax + by + c = 0

a = 1 , b = -1/2 , c = -p

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

=> m1 = - [ 1 /( -1/2 ) ]

m1 = 2 -----( 1 )

ii ) Given ax + 5 = 3y

=> ax - 3y + 5 = 0

Slope of the line ( m2 ) = - a/(-3)

m2 = a/3 ----( 2 )

According to the problem given ,

m1 = m2

=> 2 = a/3

=> 2 × 3 = a

=> a = 6

Therefore b,

a = 6

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