Home
Class 12
MATHS
If the slopes of the lines given by ax^(...

If the slopes of the lines given by `ax^(2)+2hxy+by^(2)=0` are in the ratio `3:1`, then `h^(2)=`

A

`(ab)/(3)`

B

`(4ab)/(3)`

C

`(4a)/(3b)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `y=m_1xand y=m_2x` be the lines represented by the given equation.
Then , `m_1+m_2=-(2h)/(b)and m_(1)m_(2)=(a)/(b)`
We have , `m_1:m_2=3:1rArr m_1=3m_2`
`therefore m_1+m_2=-(2h)/(b) and m_1m_2=(a)/(b)`
`rArr 4m_2=-(2h)/(b) and 3m_(2)^(2)=(a)/(b)`
`rArr m_2=-(h)/(2b)and 3m_(2)^(2)=(a)/(b)`
`rArr 3(-(h)/(2b))=(a)/(b)rArr h^2=(4ab)/(3)`
Promotional Banner

Topper's Solved these Questions

  • PAIR OR STRAIGHT LINES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PRACTICE EXCERCISE (Excercise 1) (Topical Problems) (General Equation of Second Degree)|20 Videos

  • PAIR OR STRAIGHT LINES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Excercise 2 (MISCELLANEOUS PROBLEMS)|85 Videos

  • MOCK TEST 5

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MCQS|50 Videos

  • PLANE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|9 Videos

Similar Questions

Explore conceptually related problems

If the slopes of the line given by 6x^(2)+2hxy+y^(2)=0 are in the ratio 1:2 , then h=

If the slopes of the lines 3x^(2) + 2hxy + 4y^(2)=0 are in the ration 3:1 , then h equals

If one of the lines given by ax^(2)+2hxy+by^(2)=0 is 4x-5y=0 then

If h^(2)=ab then slopes of lines ax^(2)+2hxy+by^(2)=0 are in the ratio

The slopes of the lines represented by x^(2) + 2hxy + 2y^(2) = 0 are in the ratio 1 : 2, then find 'h'.

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

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

If the slopes of one of the line given by ax^(2)+2hxy+by^(2)=0 is three times the other, then

If the slope of one of the line given by ax^(2)+2hxy+by^(2)=0 is four times the other, then

The ratio of the slopes of the lines represented by ax^(2)+2hxy+by^(2)=0 is 2:3 , then h^(2):ab=