English

Find the separate equation of the line represented by the following equation: x2 - 4y2 = 0

Advertisements
Advertisements

Question

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

x2 - 4y2 = 0

Sum
Advertisements

Solution

x2 - 4y2 = 0

∴ x2 - (2y)2 = 0

∴ (x - 2y)(x + 2y) = 0

the separate equations of the lines are

x - 2y = 0  and x + 2y = 0

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 3.2 | 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 line passing through (−1, 2), one is parallel to x + 3y − 1 = 0 and other is perpendicular to 2x − 3y − 1 = 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 


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

xy + y2 = 0 


Choose correct alternatives:

If the equation 3x2 – 8xy + qy2 + 2x + 14y + p = 1 represents a pair of perpendicular lines, then the values of p and q are respectively ______.


Choose correct alternatives:

If slope of one of the lines ax2 + 2hxy + by2 = 0 is 5 times the slope of the other, then 5h2 = ______


Choose correct alternatives:

If distance between lines (x - 2y)2 + k(x - 2y) = 0 is 3 units, then k = ______.


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 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 (-1, 2) and perpendicular to the lines  x + 2y + 3 = 0 and 3x - 4y - 5 = 0


Show that the following equations represent a pair of line:

x2 - 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:

3x2 - y2 = 0


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

2x2 + 2xy - y2 = 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 k, if the sum of the slopes of the lines given by x2 + kxy − 3y2 = 0 is equal to their product.


Find k, if one of the lines given by 3x2 - kxy + 5y2 = 0 is perpendicular to the line 5x + 3y = 0.


Find the joint equation of the pair of lines through the origin and making an equilateral triangle with the line x = 3.


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


Show that the following equation represents a pair of line. Find the acute angle between them:

(x - 3)2 + (x - 3)(y - 4) - 2(y - 4)2 = 0


Show that the combined equation of the pair of lines passing through the origin and each making an angle α with the line x + y = 0 is x2 + 2(sec 2α)xy + y2 = 0


Find the condition that the equation ay2 + bxy + ex + dy = 0 may represent a pair of lines. 


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


Find the joint equation of the line passing through the origin and having slopes 1 + `sqrt3` and 1 - `sqrt3`


The joint equation of pair of lines through the origin, each of which makes an angle of 60° with Y-axis, is ______ 


The joint equation of pair of lines having slopes `1+sqrt2` and `1-sqrt2` and passing through the origin is ______.


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


The line 5x + y – 1 = 0 coincides with one of the lines given by 5x2 + xy – kx – 2y + 2 = 0 then the value of k is ______.


If `x^2/a + y^2/b + (2xy)/h` = 0 represents a pair of lines and slope of one line is twice the other, then find the value of ab : h2.


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×