Question

MATHEMATICS
Question(22)
7
If the distance between the lines 2x + y + k = 0, 6x + 3y + 2 = 0 is
then the value of kis​

Answer 1

Answer:

2x+y+k=0

6x + 3y + 2 = 0

3(2x+y+k)=0

6x+3y+k=0

6x+3y+2=0

- - - -

_________

0-0+k-2=0

k=2

Mark as branilist

Answer 2

Answer:

k = 3

Step-by-step explanation:

Steps to Calculate The Distance Between Two Lines

• Check whether the given equations of parallel lines are in slope-intercept form (i.e. y= mx + c) or not.

• Also, if the equations of lines are given in the slope-intercept form the slope value should be common for both lines.

• Now find the value of interception point (c1 and c2) and find the value of slope for both the lines.

• Substitute the values in the slope-intercept equation to calculate the value of y.
• In the end, put all the values in the distance formula discussed below to find the distance between two lines.

2x + y + k = 0     ..............(1)

a1 = 2, b1 = 1, c1 = k

6x + 3y + 2 = 0  

Or Dividing the equation by 3

2x + y + 2/3 = 0     ..................(2)

a2 = 2, b2 = 1, c2 = 2/3

Distance(D)  is given as 7/3√5

D = c1 - c2/√a² + b²

a = 2, b = 1, c1 = k, c2 = 2/3

On substituing the values of c1, c2, a, b & c, also D value in the above formula we get,

7/3√5 =  k - 2/3/ √2² + 1²

7/3√5 = 3k - 2 / 3/√5

7/3√5 = 3k -2/3√5

eliminating 3√5 on both the sides

7 = 3k - 2

7 + 2 = 3k

9 = 3k

or, k = 9/3 = 3

Thus, k = 3