Acute Angle Between the Lines

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`

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.

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`

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 the angle between the lines `barr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk)` and `barr=5 hati-2hatk+mu(3hati+2hatj+6hatk)`

find the acute angle between the lines
x² – 4xy + y² = 0.

Find 'k' if the sum of slopes of lines represented by equation x² + kxy − 3y² = 0 is twice their product.

Find ‘k’, if the equation kxy + 10x + 6y + 4 = 0 represents a pair of straight lines.