Q4 of 112 Page 166

If the straight lines and ax + 5 = 3y are parallel, then find a.

Given: The straight lines are and ax + 5 = 3y are parallel.

Since the lines are parallel their slopes should be equal.

Now,

⇒ y = 2(x–p)

⇒ y = 2x –2p

⇒ m1 = 2

ax + 5 = 3y

⇒ 3y = ax + 5

⇒

Now as the lines are parallel ,m1 = m2

⇒

⇒ 2×3 = a

⇒ a = 6

Show that the straight lines x + 2y + 1 = 0 and 3x + 6y + 2 = 0 are parallel.

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Find the values of p for which the straight lines 8px + (2 – 3p)y + 1 = 0 and px + 8y – 7 = 0 are perpendicular to each other.