IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

dabbu

find the condition that the diagonals of the parralogram formed by the lines:

ax + by +c = 0 ;ax + by + c' + 0 ;a'x + b'y + c = 0 and a'x + b'y + c' = 0

are at right angles. also find the equation to the diagonals of the parralogram

waterdemon

Here is the solution:

Yuo have asked for the condition for which the diagonals

are perpendicular to each other.

Since the diagonals have to be perpendicular to each

other so the given quadrilateral has to be a "Rhombus".

For Rhombus only one condition can be applied that is :

"The opposite sides of Rhombus are parallel and distance

between two pairs of parallel sides in a Rhombus are '='.

Therefore,

l (c'-c)/(a²+b²)^1/2 l = l (c'-c)/(a'²+b'²)^1/2

Now on solving you will get the equation for the condition

for diagonals to be perpendicular as:-

a²+b²=a'²+b'²

Hope you find it useful.

plZ rate me for my efforts.

Cheers!!!!!!!!!!!!!!

krishna.gopal

Perfect answer nikhil

spideyunlimited

yup neat .