Answer to Question #137925 in Analytic Geometry for Rhea Marzan

Question #137925
Find the equation of the line that is parallel to 4x-5y = 2 and whose distance from the
given line is 5.
1
Expert's answer
2020-10-18T17:05:35-0400

Since, equation of parallel line to ax+by+c=0 has of the form ax+by+c'=0

Now, In this case equation of parallel line to 4x-5y-2=0 has the form 4x-5y+c'=0

We also know that distance between two parallel line is


d=cca2+b2d=\frac{|c-c'|}{\sqrt{a^2+b^2}}

Thus,


5=2c42+52    541=c+2    c=±54125=\frac{|-2-c'|}{\sqrt{4^2+5^2}}\\\implies 5\sqrt{41}=|c'+2|\\ \implies c'=\pm5\sqrt{41}-2

Thus, equation of parallel lines are


4x5y±5412=04x-5y\pm 5\sqrt{41}-2=0


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