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 ______

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 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 


Choose correct alternatives:

Auxiliary equation of 2x2 + 3xy - 9y2 = 0 is


Choose correct alternatives:

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


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 h2 = ab, then slopes of lines ax2 + 2hxy + by2 = 0 are in the ratio


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:

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.


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:

6x2 - 5xy - 6y2 = 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

2x2 - 3xy - 9y2 = 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 3x2 + kxy - y2 = 0 is zero.


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 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. 


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. 


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.


If equation ax2 - y2 + 2y + c = 1 represents a pair of perpendicular lines, then find a and c.


The combined equation of the lines through origin and perpendicular to the pair of lines 3x2 + 4xy − 5y2 = 0 is ______


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 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 ______.


The combined equation of the lines which pass through the origin and each of which makes an angle of 30° with the line 3x + 2y – 11 = 0 is ______.


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.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×