If the slopes of the lines given by the equat | vedclass

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

Question

(D) Let the slopes of the lines be $m_1$ and $m_2$. The equation $ax^2+2hxy+by^2=0$ represents two lines passing through the origin.We have the sum of

Vedclass · Accepted Answer

$16:15$

Vedclass · Answer

(D) Let the slopes of the lines be $m_1$ and $m_2$. The equation $ax^2+2hxy+by^2=0$ represents two lines passing through the origin.We have the sum of slopes $m_1+m_2 = -\frac{2h}{b}$ and the product of slopes $m_1m_2 = \frac{a}{b}$.Given the ratio of slopes is $m_1:m_2 = 5:3$,let $m_1 = 5k$ and $m_2 = 3k$.Then $m_1+m_2 = 8k = -\frac{2h}{b} \Rightarrow k = -\frac{h}{4b}$.And $m_1m_2 = 15k^2 = \frac{a}{b}$.Substituting $k$ in the product equation: $15(-\frac{h}{4b})^2 = \frac{a}{b}$.$15 	imes \frac{h^2}{16b^2} = \frac{a}{b}$.$\frac{15h^2}{16b^2} = \frac{a}{b} \Rightarrow \frac{h^2}{ab} = \frac{16}{15}$.Thus,the ratio $h^2:ab$ is $16:15$.

If the slopes of the lines given by the equation $ax^2+2hxy+by^2=0$ are in the ratio $5:3$,then the ratio $h^2:ab$ is:

Similar Questions

Acetaldehyde cannot give:

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\frac{\pi}{3}$. Then,the perimeter of the triangle is

Which of the following vitamins is water-soluble?

Let $\vec{V} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{W} = \hat{i} + 3\hat{k}$. If $\vec{U}$ is a unit vector,then the maximum value of the scalar triple product $[\vec{U} \, \vec{V} \, \vec{W}]$ is:

The proposition $(p$ $\Rightarrow \;\sim p) \wedge (\sim p$ $\Rightarrow p)$ is a

Vedclass Test Series

Exam Paper Generator

Online Exam Module