Advertisements
Advertisements
Question
Find 'k' if the sum of slopes of lines represented by equation x2 + kxy − 3y2 = 0 is twice their product.
Solution
Comparing the equation x2 + kxy – 3y2 = 0 with ax2 + 2hxy + by2 = 0, we get, a = 1, 2h = k, b = −3.
Let m1 and m2 be the slopes of the lines
represented by x2 + kxy − 3y2 = 0.
∴ m1 + m2 = `(-2h)/b = -k/((-3)) = k/3`
and m1m2 = `a/b = 1/((-3)) = -1/3`
Now, m1 + m2 = 2(m1m2) ..(Given)
∴ `k/3 = 2(-1/3)`
∴ k = −2
APPEARS IN
RELATED QUESTIONS
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`
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
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`
