हिंदी

Find the combined equation of the following pair of line: x + 2y - 1 = 0 and x - 3y + 2 = 0

Advertisements
Advertisements

प्रश्न

Find the combined equation of the following pair of line:

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

योग
Advertisements

उत्तर

The combined equation of the lines x + 2y - 1 = 0 and x - 3y + 2 = 0 is

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

∴ x2 - 3xy + 2x + 2xy - 6y2 + 4y - x + 3y - 2 = 0

∴ x2 - xy - 6y2 + x + 7y - 2 = 0

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Pair of Straight Lines - Exercise 4.1 [पृष्ठ ११९]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 4 Pair of Straight Lines
Exercise 4.1 | Q 1.2 | पृष्ठ ११९

संबंधित प्रश्न

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:

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 the following equation:

3x2 − 4xy = 0 


Choose correct alternatives:

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


If the slope of one of the two lines given by `"x"^2/"a" + "2xy"/"h" + "y"^2/"b" = 0` is twice that of the other, then ab : h2 = ______.


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


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 = ______


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 origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18


Show that the following equations represents a pair of line:

x2 + 2xy - y2 = 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:

x2 + 7xy - 2y2 = 0


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

6x2 - 5xy - 6y2 = 0


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

x2 - 4y2 = 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 k, if the sum of the slopes of the lines given by 3x2 + kxy - y2 = 0 is zero.


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


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

2x2 + xy - y2 + x + 4y - 3 = 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. 


Prove that the combined of the pair of lines passing through the origin and perpendicular to the lines ax2 + 2hxy + by2 = 0 is bx2 - 2hxy + ay2 = 0.


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


The joint equation of pair of straight lines passing through origin and having slopes `(1 + sqrt2) and (1/(1 + sqrt2))` is ______.


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 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 ______.


Write the joint equation of co-ordinate axes.


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


Combined equation of the lines bisecting the angles between the coordinate axes, is ______.


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×