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ConceptAcute Angle Between the Lines

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#### Question

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

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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`

If θ is the acute angle between the lines represented by equation ax^{2} + 2hxy + by^{2} = 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.

The slopes of the lines given by 12x^{2} + bxy + y^{2} = 0 differ by 7. Then the value of b is :

(A) 2

(B) ± 2

(C) ± 1

(D) 1

Solution for concept: Acute Angle Between the Lines. For the courses 12th HSC Arts, 12th HSC Science (Computer Science), 12th HSC Science (Electronics), 12th HSC Science (General)