मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Find the joint equation of the line passing through (1, 2) and parallel to the coordinate axes - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the joint equation of the line passing through (1, 2) and parallel to the coordinate axes

बेरीज
Advertisements

उत्तर

Equations of the coordinate axes are x = 0 and y = 0

∴ the equations of the lines passing through (1, 2) and parallel to the coordinate axes are x = 1 and y = 2.

i.e. x - 1 = 0 and y - 2 = 0

∴ their combined equation is

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

∴ x(y - 2) - 1(y - 2) = 0

∴ xy - 2x - y + 2 = 0

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Pair of Straight Lines - Miscellaneous Exercise 4 [पृष्ठ १३०]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 4 Pair of Straight Lines
Miscellaneous Exercise 4 | Q 1.05 | 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 separate equation of the line represented by the following equation:

5x2 – 9y2 = 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 the following equation:

xy + 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 


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 = ______.


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:

x + y − 3 = 0 and 2x + y − 1 = 0


Find the joint equation of the line passing through the origin having slopes 2 and 3.


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


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:

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 - 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:

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


Find k, if the slope of one of the lines given by 3x2 - 4xy + ky2 = 0 is 1.


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


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


Find the combined equation of bisectors of angles between the lines represented by 5x2 + 6xy - y2 = 0.


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


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


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. 


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.


The combined equation of the lines through origin and perpendicular to the pair of lines 3x2 + 4xy − 5y2 = 0 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 joint equation of pair of lines having slopes `1+sqrt2` and `1-sqrt2` and passing through the origin is ______.


The joint equation of pair of lines having slopes 2 and 5 and passing through the origin 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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×