Question

The equations of the lines parallel to 4 x+3 y+2=04x+3y+2=0 and at a distance of 4 units from it are

Answer 1

Answer:

The eq. of the lines parallel to 4x+3 y+2=0 and at a distance of '4' units from it are ... 2:49 · Equation represents a pair of parallel lines and find distance between them. `4x^.

Answer 2

Answer:

4x + 3y + 22 = 0 and 4x + 3y - 18 =0

Step-by-step explanation:

Given:

The equation of line: 4x + 3y + 2 =0

distance: 4 units

To find:

The equation of a line parallel to the given line.

Formula used:

d = | $\frac{c1 - c2}{\sqrt{a^{2} +b^{2} } }$ |

where c1 and c2 are constant in equation like ax + by + c =0

and d is the distance between 2 lines.

Solution:

we know,

the equation of the line parallel to the given line is ax+by+k =0,

and there will be 2 line parallel to the given line one is above the given line and second is below the given line.

also, the equation of new line is 4x + 3y + k =0 (as lines are parallel hence slope is same).

∵ d = | $\frac{k - 2}{\sqrt{16 + 9} }$ | (putting the values in above formula)

=> d = | $\frac{k - 2}{ 5 }$ |

=> | $\frac{k - 2}{5}$ | = 4

=> $\frac{ k - 2}{5}$ = 4 OR $\frac{k - 2}{5}$ = -4

=> k-2 = 20  and k-2 = -20

=> k= 22 and k = -18

Now, putting the value of k in equation 4x + 3y + k =0

we get,

4x + 3y + 22 = 0 and 4x + 3y -18 = 0 are the equations of the line parallel to the given line. Ans

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