हिंदी

Find the joint equation of the line: x + y - 3 = 0 and 2x + y - 1 = 0 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the joint equation of the line:

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

योग

उत्तर

Find the joint equation of the line x + y - 3 = 0 and 2x + y - 1 = 0

(x + y - 3)(2x + y - 1) = 0

∴ 2x2 + xy - x + 2xy + y2 - y - 6x - 3y + 3 = 0

∴ 2x2 + 3xy + y2 - 7x - 4y + 3 = 0

shaalaa.com
Combined Equation of a Pair Lines
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Pair of Straight Lines - Miscellaneous Exercise 4 [पृष्ठ १३०]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 4 Pair of Straight Lines
Miscellaneous Exercise 4 | Q 1.02 | पृष्ठ १३०

संबंधित प्रश्न

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:

3y2 + 7xy = 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 + 2xy tan α - 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:

The combined equation of the coordinate axes is


Find the joint equation of the line:

x - y = 0 and x + y = 0


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


Show that the following equations represents a pair of line:

4x2 + 4xy + y2 = 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:

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


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


If the lines given by ax2 + 2hxy + by2 = 0 form an equilateral triangle with the line lx + my = 1, show that (3a + b)(a + 3b) = 4h2.


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.


Show that the combined equation of pair of lines passing through the origin is a homogeneous equation of degree 2 in x and y. Hence find the combined equation of the lines 2x + 3y = 0 and x − 2y = 0


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 the lines through the origin which forms two of the sides of the equilateral triangle having x = 2 as the third side is ______


The equation of line passing through the midpoint of the line joining the points (-1, 3, -2) and (-5, 3, -6) and equally inclined to the axes is ______.


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


Find the combined equation of the pair of lines passing through the origin and perpendicular to the lines represented by 3x2 + 2xy – y2 = 0.


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


Find the combined equation of y-axis and the line through the origin having slope 3.


Find k, if one of the lines given by kx2 – 5xy – 3y2 = 0 is perpendicular to the line x – 2y + 3 = 0


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×