If O,A,B are vertices of a triangle whose sides are given by $$5x+12y2$$−$$312x$$−$$5y2=0$$ and $$5x+12y$$−$$78=0$$ then AB $$=$$

Question

If O,A,B  are vertices of a triangle whose sides are given by  $$5x+12y2$$−$$312x$$−$$5y2=0$$ and $$5x+12y$$−$$78=0$$   then AB  $$=$$

Infinity Learn · Accepted Answer

The triangle formed by the lines $$5x+12y2$$−$$312x$$−$$5y2=0$$  and  $$5x+12y$$−$$78=0$$  is equilateral triangle. The area of The area of the equilateral triangle formed by the lines $$ax+by+c=0$$  and the pair of lines $$ax+by2$$−$$3bx$$−$$ay2=0$$  is  $$c23(a2+b2)$$ Hence, the area of the triangle is  $$7823(52+122)If$$ the length of the side of the equilateral triangle is a  then its area is  $$3a24it$$ implies $$that3a24=782352+122a2=4$$⋅$$78$$⋅$$783169=4$$⋅$$6$$⋅$$63=48Therefore$$,$$a=43$$

If $O, A, B$ are vertices of a triangle whose sides are given by ${(5 x + 12 y)}^{2} - 3 {(12 x - 5 y)}^{2} = 0$ and $5 x + 12 y - 78 = 0$ then AB =

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If O,A,B are vertices of a triangle whose sides are given by 5x+12y2−312x−5y2=0 and 5x+12y−78=0 then AB =

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If $O, A, B$ are vertices of a triangle whose sides are given by ${(5 x + 12 y)}^{2} - 3 {(12 x - 5 y)}^{2} = 0$ and $5 x + 12 y - 78 = 0$ then AB =