Question

For what value of a and b , the lines represented by equation ax^2 + xy + by^2=0 , will be inclined at 45 degrees?

Answer 1

by^2 + yx + ax^2 =0
=>y = -x + sqrt(x^2 - 4abx^2)/2 and -x -2 sqrt(x^2 - 4abx^2)/2

or y= x(-1 + sqrt(1 - 4ab)/2 and x(-1 - sqrt(1 - 4ab)/2

these are the eqns of the 2 lines

let m1 = (-1 + sqrt(1 - 4ab)/2 and m2 = (-1 - sqrt(1 - 4ab)/2
since the 2 lines are at 45 degrees to each other,we have
1 = | m1- m2 / 1+ m1 m2 |

obtain2 eqns, solve for a and b.

Answer 2

how can we equate slopes to lines?

Answer 3

didnt get your query ?

Answer 4

what are m1 and m2?

Answer 5

ok i got it

Answer 6

but we will get only 1 eq.

Answer 7

its in mod right,,so you'll get 2 eqns..

like this
if |x| = 1
then x= 1 and -1..

Answer 8

ok