Question

(b) Find the equation of line parallel to the line x + 4y - 8 =0 and at a
distance of 5 units from Origin.

Answer 1

SOLUTION

TO DETERMINE

The equation of line parallel to the line x + 4y - 8 = 0 and at a distance of 5 units from Origin.

EVALUATION

Here the given equation of the line is

x + 4y - 8 = 0

Now the equation of the line parallel to the line x + 4y - 8 = 0 is

x + 4y + k = 0 - - - - - - (1)

Now the distance from origin

$\displaystyle \sf{ = \bigg| \frac{k}{ \sqrt{ {1}^{2} + {4}^{2} } } \bigg| }$

$\displaystyle \sf{ = \bigg| \frac{k}{ \sqrt{ 17} } \bigg| }$

So by the given condition

$\displaystyle \sf{ \bigg| \frac{k}{ \sqrt{ 17} } \bigg| = 5}$

$\displaystyle \sf{ \implies k = \pm \: 5 \sqrt{17} }$

So the required equation of the line is

$\sf{x + 4y \pm \: 5 \sqrt{17} = 0}$

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