Question

if the longest give by 3x+2ky=2amd2x+5y+1=0are parallel then the value of k is​

Answer 1

For the lines to be parallel, the slopes of the lines MUST be equal.

Lines:

3x + 2ky - 2 = 0 … (1)

2x + 5y + 1 = 0 … (2)

Now, convert 1 and 2 into y = mx + c form where m is the slope.

for 1,

y = (-3/2k)x + (1/k)

for 2,

y = (-2/5)x - (1/5)

So now for both lines to be parallel, (-3/2k) must be equal to (-2/5)

Solving for k, we get {k = 15/4}

or

Condition for parallel lines is

a1/a2 = b1/b2 ≠ c1/c2 …(i)

Given lines, 3x + 2ky - 2 = 0

and 2x + 5y - 1 = 0;

Comparing with ax + by + c = 0;

Here, a1 = 3, b1 = 2k, c1 = - 2

and a2 = 2, b2 = 5, c2 = - 1

From Eq. (i), 3/2 = 2k/5

k = 15/4

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