English

Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0. - Mathematics and Statistics

Advertisements
Advertisements

Question

Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0.

Sum
Advertisements

Solution

The auxiliary equation of the lines represented by 6x2 + kxy + y2 = 0 is m2 + km + 6 = 0

Since one of the line is 2x + y = 0 whose slope is m = - 2.

∴ m = - 2 is the root of the auxiliary equation m2 + km + 6 = 0.

∴ (-2)2 + k(-2) + 6 = 0

∴ 4 - 2k + 6 = 0

∴ 2k = 10

∴ k = 5 

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Pair of Straight Lines - Miscellaneous Exercise 4 [Page 131]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 4 Pair of Straight Lines
Miscellaneous Exercise 4 | Q 5.7 | Page 131

RELATED QUESTIONS

Find the combined equation of the following pair of lines:

2x + y = 0 and 3x − y = 0


Find the combined equation of the following pair of line:

x + 2y - 1 = 0 and x - 3y + 2 = 0


Find the combined equation of the following pair of lines passing through point (2, 3) and parallel to the coordinate axes.


Find the combined equation of the following pair of lines:

Passing through (2, 3) and perpendicular to the lines 3x + 2y – 1 = 0 and x – 3y + 2 = 0.


Find the separate equation of the line represented by the following equation:

`3"x"^2 - 2sqrt3"xy" - 3"y"^2 = 0`


Find the separate equation of the line represented by the following equation:

x2 + 2(cosec α)xy + y2 = 0


Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by following equation:

5x2 - 8xy + 3y2 = 0 


Choose correct alternatives:

Auxiliary equation of 2x2 + 3xy - 9y2 = 0 is


Choose correct alternatives:

If two lines ax2 + 2hxy + by2 = 0 make angles α and β with X-axis, then tan (α + β) = _____.


The joint equation of the lines through the origin and perpendicular to the pair of lines 3x2 + 4xy – 5y2 = 0 is _______.


The area of triangle formed by the lines x2 + 4xy + y2 = 0 and x - y - 4 = 0 is ______.


Choose correct alternatives:

The combined equation of the coordinate axes is


Choose correct alternatives:

If h2 = ab, then slopes of lines ax2 + 2hxy + by2 = 0 are in the ratio


Find the joint equation of the line passing through the origin and having inclinations 60° and 120°.


Find the joint equation of the line passing through (3, 2) and parallel to the lines x = 2 and y  = 3.


Find the joint equation of the line which are at a distance of 9 units from the Y-axis.


Find the joint equation of the line passing through the point (3, 2), one of which is parallel to the line x - 2y = 2, and other is perpendicular to the line y = 3.


Find the joint equation of the line passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18


Show that the following equations represents a pair of line:

4x2 + 4xy + y2 = 0


Show that the following equations represent a pair of line:

x2 + 7xy - 2y2 = 0


Show that the following equations represent a pair of line:

`"x"^2 - 2sqrt3"xy" - "y"^2 = 0`


Find the separate equation of the line represented by the following equation:

6x2 - 5xy - 6y2 = 0


Find the joint equation of the pair of a line through the origin and perpendicular to the lines given by

x2 + 4xy - 5y2 = 0


Find the joint equation of the pair of a line through the origin and perpendicular to the lines given by

2x2 - 3xy - 9y2 = 0


Find the joint equation of the pair of a line through the origin and perpendicular to the lines given by

x2 + xy - y2 = 0


Find k, if the sum of the slopes of the lines given by x2 + kxy − 3y2 = 0 is equal to their product.


Find k, if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.


Find a if the sum of the slopes of lines represented by ax2 + 8xy + 5y2 = 0 is twice their product.


If the line 4x - 5y = 0 coincides with one of the lines given by ax2 + 2hxy + by2 = 0, then show that 25a + 40h + 16b = 0


If the line x + 2 = 0 coincides with one of the lines represented by the equation x2 + 2xy + 4y + k = 0, then prove that k = - 4. 


If equation ax2 - y2 + 2y + c = 1 represents a pair of perpendicular lines, then find a and c.


Find k if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.


Write the separate equations of lines represented by the equation 5x2 – 9y2 = 0


Find the joint equation of the pair of lines through the origin and perpendicular to the lines given by 2x2 + 7xy + 3y2 = 0


The distance between the lines represented by the equation 4x² + 4xy + y² − 6x − 3y − 4 = 0 is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×