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

The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis is ______ - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis is ______  

पर्याय

  • x2 + y2 = 0

  • xy = 1

  • x2 − y2 = 0

  • x2 + xy =0 

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

x2 − y2 = 0 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.4: Pair of Lines - MCQ

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 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:

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 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 


Choose correct alternatives:

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

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 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


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

x2 - 4y2 = 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 one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0.


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


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


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


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 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. 


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


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 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 ______.


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 ______.


Write the joint equation of co-ordinate axes.


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.


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×