(C) Let the slopes of the two lines be $m$ and $2m$.From the equation $ax^2+2hxy+by^2=0$,we have:Sum of slopes: $m_1+m_2 = m+2m = 3m = -\frac{2h}{b} \

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

(C) Let the slopes of the two lines be $m$ and $2m$.From the equation $ax^2+2hxy+by^2=0$,we have:Sum of slopes: $m_1+m_2 = m+2m = 3m = -\frac{2h}{b} \Rightarrow m = -\frac{2h}{3b}$.Product of slopes: $m_1 \times m_2 = m \times 2m = 2m^2 = \frac{a}{b}$.Substituting the value of $m$ into the product equation:$2(-\frac{2h}{3b})^2 = \frac{a}{b}$$2(\frac{4h^2}{9b^2}) = \frac{a}{b}$$\frac{8h^2}{9b^2} = \frac{a}{b}$$8h^2 = 9ab$.

Class 11 Mathematics Pair of straight lines Equation of pair of straight lines

Easy

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

MHT CET 2022 All MHT CET

MHT CET 2018 All MHT CET

A
$8h=9ab^2$
B
$8h^2=9ab^2$
C
$8h^2=9ab$
D
$8h=9ab$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Pair of straight lines

Subtopic

Equation of pair of straight lines

Previous Year

MHT CET 2022 Paper All MHT CET years →

Previous Year

MHT CET 2018 Paper All MHT CET years →

$A$ homogeneous equation of second degree in $x$ and $y$ represents which of the following?

EasyAP EAMCET 2020

View Solution

For what value of $p$ does the equation $y^2 + xy + px^2 - x - 2y = 0$ represent two straight lines?

Medium

View Solution

The equation of the pair of lines passing through the origin and parallel to the lines $y = m_1x + c_1$ and $y = m_2x + c_2$ is:

Medium

View Solution

The value of $\lambda$ for which the equation $x^2 - \lambda xy + 2y^2 + 3x - 5y + 2 = 0$ represents a pair of straight lines is

Medium

View Solution

If the sum of the slopes of the lines represented by the equation $x^2 - 2xy \tan A - y^2 = 0$ is $4$,then $\angle A = $

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

$A$ homogeneous equation of second degree in $x$ and $y$ represents which of the following?

For what value of $p$ does the equation $y^2 + xy + px^2 - x - 2y = 0$ represent two straight lines?

The equation of the pair of lines passing through the origin and parallel to the lines $y = m_1x + c_1$ and $y = m_2x + c_2$ is:

The value of $\lambda$ for which the equation $x^2 - \lambda xy + 2y^2 + 3x - 5y + 2 = 0$ represents a pair of straight lines is

If the sum of the slopes of the lines represented by the equation $x^2 - 2xy \tan A - y^2 = 0$ is $4$,then $\angle A = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module