Question

If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then

• A. 8h2 = 9ab
• B. 8h = 9ab
• C. 8h2 = 9ab2
• D. 8h = 9ab2

Answer 1

Answer: (A)

8h2 = 9ab

Answer 2

ax2 + 2hxy + by2 =0
m1 + m2 = -2h/b
m1m2 = $\frac {a}{b}$
Given:
m1 = 2m2
put m1 = 2m2
2m2 + m2 = $\frac {- 2h}{b}$
3m2 = $\frac {- 2h}{b}$
m2 = $\frac {- 2h}{3b}$
and 2m2 = $\frac {a}{b}$
m2 = $\frac {a}{2b}$
Now, $(\frac {- 2h}{3b})^2$ = $\frac {a}{2b}$
$\frac {4h^2}{9b^2}$ = $\frac {a}{2b}$
8h2 = 9ab
Therefore the correct option is (A) 8h2 = 9ab