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

(B) Let the slopes of the lines be $m_{1}$ and $m_{2}$.Given the equation $ax^{2} + 2hxy + by^{2} = 0$,we have $m_{1} + m_{2} = \frac{-2h}{b}$ and $m_

Vedclass · Accepted Answer

$16:15$

Vedclass · Answer

(B) Let the slopes of the lines be $m_{1}$ and $m_{2}$.Given the equation $ax^{2} + 2hxy + by^{2} = 0$,we have $m_{1} + m_{2} = \frac{-2h}{b}$ and $m_{1}m_{2} = \frac{a}{b}$.Given the ratio of slopes is $m_{1}:m_{2} = 5:3$,let $m_{1} = 5k$ and $m_{2} = 3k$.Then $m_{1} + m_{2} = 8k = \frac{-2h}{b} \Rightarrow k = \frac{-h}{4b}$.Also $m_{1}m_{2} = 15k^{2} = \frac{a}{b}$.Substituting $k$ in the second equation: $15 \left( \frac{-h}{4b} \right)^{2} = \frac{a}{b}$.$15 \left( \frac{h^{2}}{16b^{2}} \right) = \frac{a}{b}$.$\frac{15h^{2}}{16b} = a$.Therefore,$\frac{h^{2}}{ab} = \frac{16}{15}$.

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

The value of $k$ so that the equation $2x^2 + 5xy + 3y^2 + 6x + 7y + k = 0$ represents a pair of straight lines is:

The gradient of one of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is twice that of the other. Then:

If two of the three lines represented by the equation $ax^3 + bx^2y + cxy^2 + dy^3 = 0$ are perpendicular,then:

The equation of the pair of straight lines perpendicular to the pair $2 x^2+3 x y+2 y^2+10 x+5 y=0$ and passing through the origin is $..........$

If the equation $3x^{2}+10xy+3y^{2}+16y+k=0$ represents a pair of lines,then the value of $k$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module