B Sc 2nd Year 3rd Semester Mathematics Pair of Straight lines Analytical Geometry Most Important Questions
Mathematics –HC
Analytical Geometry
Pair of Straight lines
1. Show that the equation represents a pair of straight lines. Find the straight lines and the angle between them.
2. Show that the equation to the pair of straight lines through the origin perpendicular to the pair of straight lines 〖ax〗^2+2hxy+〖by〗^2=0 ; 〖bx〗^2-2hxy+〖ay〗^2=0
3. Find the condition that one of the straight lines given by 〖ax〗^2+2hxy+〖by〗^2=0 may coincide with one of the straight lines given by a^/ x^2+2h^/ xy+b^/ y^2=0
4. Find the equation of the pair of straight lines perpendicular to the pair of lines given by 〖ax〗^2+2hxy+〖by〗^2=0
5. Prove that every homogeneous second degree equation always represent a pair of straight line passing through the origin.
6. Under what condition the lines represented by a^2+2hxy+〖by〗^2=0 will be perpendicular to each other.
7. Under what condition, the lines represented by 〖ax〗^2+2hxy+〖by〗^2=0 will be coincident.
8. What is the locus represented by the equation x^2-5xy+〖6y〗^2=0?
9. Show that the equation x^2+3xy+〖2y〗^2=0 represents a pair of straight lines. Find these straight lines and the angle between them.
10. Show that the equation 〖12x〗^2-7xy-〖12y〗^2=0 represents a pair of perpendicular straight lines. Find these straight lines.
11. Find the angle between the lines x^2+xy-〖6y〗^2=0
12. Find the equation of the bisectors of the angles between the lines x^2-4xy-y^2=0
13. Write the condition for which the general equation of second degree 〖ax〗^2+2hxy+〖by〗^2+2gx+2fy+c=0 represents a pair of straight line.
14. Show that 〖14x〗^2+29xy+〖12y〗^2-31x-14y-10=0 represents a pair of straight lines.
15. Show that x^2+6xy+〖9y〗^2-5x-15y+6=0 represents a pair of parallel lines and find the distance between them.
17. Show that 〖6x〗^2-5xy-〖6y〗^2+14x+5y+4=0 represents a pair of perpendicular lines.
18. For what value of λ does λxy-8x+9y-12=0 represents a pair of lines.
B.Sc 3rd semester mathematics solutions. B Analytical Geometry
Pair of Straight lines
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