1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider a line pair 2 x2+3 x y-2 y2-10 x+15 y-28=0 and another line L passing through origin with gradient 3. The line pair and line L form a triangle whose vertices are A , B and C. Sum of the contangents of the interior angles of the triangle ABC is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Consider a line pair $2 x^2+3 x y-2 y^2-10 x+15 y-28=0$ and another line $L$ passing through origin with gradient 3. The line pair and line $L$ form a triangle whose vertices are $A , B$ and $C$.
Sum of the contangents of the interior angles of the triangle $ABC$ is

Straight Lines

Solution:

The two lines are
$(2 x - y +4)( x +2 y -7)=0 $
$\text { Line Lis } $
$y = 3x$
$ \angle B =90^{\circ} $
$\therefore \cot B =0$
$ \cot A =\frac{21 \times \sqrt{5}}{\sqrt{5} \times 3}=7$
image
$ \cot C=\frac{3 \times \sqrt{5}}{\sqrt{5} \times 21}=\frac{1}{7} $
$\therefore \text { sum of cotangents }=7+\frac{1}{7}=\frac{50}{7}$