Advertisements
Advertisements
प्रश्न
Find the separate equation of the line represented by the following equation:
3x2 - y2 = 0
उत्तर
3x2 - y2 = 0
∴ `(sqrt3"x")^2 - "y"^2 = 0`
∴ `(sqrt3"x" - "y")(sqrt3"x" + "y") = 0`
the separate equations of the lines are
`sqrt3"x" - "y" = 0` and `sqrt3"x" + "y" = 0`
APPEARS IN
संबंधित प्रश्न
Find the combined equation of the following pair of line:
2x + y = 0 and 3x − y = 0
Find the combined equation of the following pair of lines passing through point (2, 3) and parallel to the coordinate axes.
Find the separate equation of the line represented by the following equation:
3y2 + 7xy = 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 following equation:
5x2 - 8xy + 3y2 = 0
Choose correct alternatives:
Auxiliary equation of 2x2 + 3xy - 9y2 = 0 is
Choose correct alternatives:
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 ______.
Find the joint equation of the line passing through (1, 2) and parallel to the coordinate axes
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 represent a pair of line:
`"x"^2 - 2sqrt3"xy" - "y"^2 = 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 the sum of the slopes of the lines given by x2 + kxy − 3y2 = 0 is equal to their product.
Find k, if one of the lines given by 3x2 - kxy + 5y2 = 0 is perpendicular to the line 5x + 3y = 0.
Find k, if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.
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.
Find an if the sum of the slope of lines represented by ax2 + 8xy + 5y2 = 0 is twice their product.
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 equation ax2 - y2 + 2y + c = 1 represents a pair of perpendicular lines, then find a and c.
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 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 equation of line passing through the midpoint of the line joining the points (-1, 3, -2) and (-5, 3, -6) and equally inclined to the axes is ______.
The joint equation of pair of lines having slopes `1+sqrt2` and `1-sqrt2` 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 ______.
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 k, if one of the lines given by kx2 – 5xy – 3y2 = 0 is perpendicular to the line x – 2y + 3 = 0
