(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 →

If two sides of a triangle are represented by $x^2 - 7xy + 6y^2 = 0$ and the centroid is $(1, 0)$,then the equation of the third side is

Difficult

View Solution

The equation of the pair of lines passing through the point $(2,1)$ and perpendicular to the pair of lines $4xy + 2x + 6y + 3 = 0$ is:

MediumAP EAMCET 2017

View Solution

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

Difficult

View Solution

If $m_1$ and $m_2$ $(m_1 > m_2)$ are the slopes of the lines represented by $5x^2 - 8xy + 3y^2 = 0$,then $m_1 : m_2$ equals

MediumAP EAMCET 2021

View Solution

Find the equation of the pair of lines passing through the origin and perpendicular to the pair of lines given by $5x^2 - 7xy - 3y^2 = 0$.

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

If two sides of a triangle are represented by $x^2 - 7xy + 6y^2 = 0$ and the centroid is $(1, 0)$,then the equation of the third side is

The equation of the pair of lines passing through the point $(2,1)$ and perpendicular to the pair of lines $4xy + 2x + 6y + 3 = 0$ is:

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

If $m_1$ and $m_2$ $(m_1 > m_2)$ are the slopes of the lines represented by $5x^2 - 8xy + 3y^2 = 0$,then $m_1 : m_2$ equals

Find the equation of the pair of lines passing through the origin and perpendicular to the pair of lines given by $5x^2 - 7xy - 3y^2 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module