If the slope of one of the lines represented | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For the pair of lines $ax^2+2hxy+by^2=0$,let the slopes be $m_1$ and $m_2$.We have $m_1+m_2 = -\frac{2h}{b}$ and $m_1m_2 = \frac{a}{b}$.Given that

Vedclass · Accepted Answer

$9:8$

Vedclass · Answer

(C) For the pair of lines $ax^2+2hxy+by^2=0$,let the slopes be $m_1$ and $m_2$.We have $m_1+m_2 = -\frac{2h}{b}$ and $m_1m_2 = \frac{a}{b}$.Given that one slope is twice the other,let $m_1 = 2m_2$.Substituting this into the sum of slopes: $2m_2 + m_2 = -\frac{2h}{b}$ $\Rightarrow 3m_2 = -\frac{2h}{b}$ $\Rightarrow m_2 = -\frac{2h}{3b}$.Substituting into the product of slopes: $m_1m_2 = (2m_2)m_2 = 2m_2^2 = \frac{a}{b}$.Thus,$2(-\frac{2h}{3b})^2 = \frac{a}{b} \Rightarrow 2(\frac{4h^2}{9b^2}) = \frac{a}{b}$.$\frac{8h^2}{9b^2} = \frac{a}{b} \Rightarrow \frac{h^2}{ab} = \frac{9}{8}$.Therefore,$h^2:ab = 9:8$.

If the slope of one of the lines represented by $ax^2+2hxy+by^2=0$ is twice that of the other,then $h^2:ab$ is

Similar Questions

If the slope of one of the lines given by $ax^2 + 2hxy + by^2 = 0$ is $5$ times the other,then

The equation $2y^2 - xy - x^2 + 6x - 8 = 0$ represents

The equation $xy + a^2 = a(x + y)$ represents

The value of $p$ for which the equation $x^2+pxy+y^2-5x-7y+6=0$ represents a pair of straight lines is:

The value of $p$ for which the equation $x^2+pxy+y^2-5x-7y+6=0$ represents a pair of straight lines is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module