English

Write the joint equation of co-ordinate axes.

Advertisements
Advertisements

Question

Write the joint equation of co-ordinate axes.

Sum
Advertisements

Solution

As we know that,

  • In the coordinate axes, on the x-axis, the value of y always stays constant and the value of x keeps changing.
  • Similarly, on the y-axis, the value of x stays constant and the value of y keeps changing.

Here,

Equation of coordinates,

for x-axis,

y = 0  `\implies` equation (1)

for y-axis,

x = 0  `\implies` equation (2)

now,

To get the combined equation we will multiply equations (1) and (2).

xy = 0

Hence the joint equation of coordinates axes is xy = 0

shaalaa.com
  Is there an error in this question or solution?
2022-2023 (March) Official

RELATED QUESTIONS

Find the combined equation of the following pair of lines:

2x + y = 0 and 3x − y = 0


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

x2 - 4xy = 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 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 


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) = _____.


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


Choose correct alternatives:

If slope of one of the lines ax2 + 2hxy + by2 = 0 is 5 times the slope of the other, then 5h2 = ______


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 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 point (3, 2), one of which is parallel to the line x - 2y = 2, and other is perpendicular to the line y = 3.


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:

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 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.


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 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 straight lines passing through origin and having slopes `(1 + sqrt2) and (1/(1 + sqrt2))` 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 ______


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 ______.


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.


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×