Advertisements
Advertisements
Question
The slopes of the lines given by 12x2 + bxy + y2 = 0 differ by 7. Then the value of b is :
(A) 2
(B) ± 2
(C) ± 1
(D) 1
Solution
(C)
Given equation is `12x^2+bxy-y^2=0`
Comparing with `Ax^2+2Hxy+By^2=0 ," we get"`
A = 12, 2H = b, B = -1
`m_1+m_2=(-2H)/B=-b/-1=b`
`and m_1m_2=A/B=12/-1=-12`
According to given condition,
`|m_1-m_2|=7`
`(m_1-m_2)^2=49`
`b^2-4(-12)=4`
`b^2=49-48`
`b=+-1`
APPEARS IN
RELATED QUESTIONS
Find 'k' if the sum of slopes of lines represented by equation x2 + kxy − 3y2 = 0 is twice their product.
If θ is the acute angle between the lines represented by equation ax2 + 2hxy + by2 = 0 then prove that `tantheta=|(2sqrt(h^2-ab))/(a+b)|, a+b!=0`
Find ‘k’, if the equation kxy + 10x + 6y + 4 = 0 represents a pair of straight lines.
If θ is the measure of acute angle between the pair of lines given by `ax^2+2hxy+by^2=0,` then prove that `tantheta=|(2sqrt(h^2-ab))/(a+b)|,a+bne0`
Show that the equation `x^2-6xy+5y^2+10x-14y+9=0 ` represents a pair of lines. Find the acute angle between them. Also find the point of intersection of the lines.
find the acute angle between the lines
x2 – 4xy + y2 = 0.
Find the angle between the lines `barr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk)` and `barr=5 hati-2hatk+mu(3hati+2hatj+6hatk)`
If a line is inclined at 60° and 30° with the X and Y-axes respectively, then the angle which it makes with Z-axis is
(A) 0
(B) `pi/4`
(C) `pi/2`
(D) `pi/6`
