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  • The straight lines <img alt="\mathrm{3 x+4 y=5 \; and\; 4 x-3 y=15}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%20x&plus;4%20y%3D5%20%5C%3B%20and%5C%3B%204%20x-3%20y%3D1

The straight lines \mathrm{3 x+4 y=5 \; and\; 4 x-3 y=15} intersect at the point A. On these lines the points B and C are chosen so that AB=AC. Find the possible equation of the line BC passing through the point (1,2).

Option: 1

\mathrm{7x+y-9=0}


Option: 2

\mathrm{x-7y+13=0}


Option: 3

Both (1) and (2)


Option: 4

None of these 


Answers (1)

best_answer

The given lines are perpendicular and as AB = AC, therefore triangle ABC is a right angled isosceles.

Hence the line BC through (1, 2) will make an angle of \pm \: 45^{\circ} with the given lines.

\pm 1=\frac{\mathrm{m+\frac{3}{4}}}{\mathrm{1-m.\frac{3}{4}}}\Rightarrow \mathrm{m}=\frac{1}{7} \text { or }-7

Its equation is  \mathrm{y-2=m(x-1)} where \mathrm{m=\frac{1}{7} \text { and }-7}

Hence the possible equation of the line BC are

\mathrm{7 x+y-9=0 \text { and } x-7 y+13=0}

Posted by

Deependra Verma

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