If the equations 4x + (k − 2)y + 3 = 0 and (k − 2)x + 9y − 5 = 0 (k > 0) are parallel, then find the value of k2 + 6.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 70.
We know that,
When two lines are parallel then
a1/a2 = b1/b2 ≠ c1/c2
here,
a1 = 4, a2 = (k - 2), b1 = (k - 2), b2 = 9, c1 = 3, and c2 = -5
Now,
⇒ 4/(k - 2) = (k - 2)/9 ≠ -3/5
⇒ 4/(k - 2) = (k - 2)/9
⇒ 36 = (k - 2)2
⇒ ±6 = k - 2
⇒ k = 8, -4
The value ok k is 8 because (k > 0)
Now, the value of k2 + 6 = 64 + 6 = 70