The lines $$2x+5y=10$$ and $$3x+4y=12$$ cuts the $$x-axis$$ at A and B respectively. A line L drawn through the point $$3$$,$$4$$ meets $$y-axis$$ at C such that the abscissae of A ,B, and ordinate of C are in geometric progression. If the equation of the line L is $$ax+by+c=0$$ then $$a+b+c$$ is

Question

The lines $$2x+5y=10$$ and $$3x+4y=12$$ cuts the  $$x-axis$$ at  A and B respectively. A line L drawn through the point $$3$$,$$4$$ meets  $$y-axis$$ at C such that the abscissae of  A ,B,   and ordinate of C  are in geometric progression. If the equation of the line L  is $$ax+by+c=0$$ then $$a+b+c$$ is

Infinity Learn · Accepted Answer

The line $$2x+5y=10$$ cuts $$x-axis$$ at $$A5$$,$$0$$ and the line  $$3x+4y=12$$  cuts  $$x-axis$$ at $$B4$$,$$0The$$ point C lies on   $$y-axis$$ , let it be  $$C0$$,kGiven  $$5$$,$$4$$,k are in geometric progressionIt implies that $$45=k4$$ Cross multiply  $$5k=16k=165Hence$$ the line  L is passing through the points  $$3$$,$$4$$,$$0$$,$$165Equation$$ of  Ly−$$4=165$$−$$40$$−$$3x$$−$$3=415x$$−$$315y$$−$$60=4x$$−$$124x$$−$$15y+48=0Hence$$, $$a+b+c=4$$−$$15+48=37$$

The lines $2 x + 5 y = 10$ and $3 x + 4 y = 12$ cuts the x-axis at A and B respectively. A line L drawn through the point $(3, 4)$ meets y-axis at C such that the abscissae of A ,B, and ordinate of C are in geometric progression. If the equation of the line L is $ax + by + c = 0$ then $a + b + c$ is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The lines 2x+5y=10 and 3x+4y=12 cuts the x-axis at A and B respectively. A line L drawn through the point 3,4 meets y-axis at C such that the abscissae of A ,B, and ordinate of C are in geometric progression. If the equation of the line L is ax+by+c=0 then a+b+c is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material