straight line:)

Find the equation of the bisector of the angle between 4x+y-7=0 and x-4y+3=0 which contains the origin.

2 Answers

same as your previous question (almost)

First find the two bisectors using distance formula.

Then take a point on the line (any arbitrary point on the bisector)

Cheeck if the product of distance (algebraic) is of the same sign as the value for origin.

it is given by the formula
\frac{a_{1}x+b_{1}y+c_{1}}{\sqrt{a_{1}^{2}+b_{1}^{2}}}=\frac{a_{2}x+b_{2}y+c_{2}}{\sqrt{a_{2}^{2}+b_{2}^{2}}}

so from given two equations it becomes
\frac{4x+y-7}{\sqrt{4^{2}+1^{2}}}=\frac{x-4y+3}{\sqrt{1^{2}+4^{2}}}

â†’ equation required is 3x + 5y - 10 = 0

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