Advertisements
Advertisements
प्रश्न
Find the separate equation of the line represented by the following equation:
3x2 - y2 = 0
Advertisements
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 lines:
2x + y = 0 and 3x − y = 0
Find the separate equation of the line represented by the following equation:
x2 + 2(cosec α)xy + y2 = 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:
5x2 + 2xy - 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:
3x2 − 4xy = 0
Choose correct alternatives:
Auxiliary equation of 2x2 + 3xy - 9y2 = 0 is
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 distance between lines (x - 2y)2 + k(x - 2y) = 0 is 3 units, then k = ______.
Find the joint equation of the line:
x - y = 0 and x + y = 0
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
Find the separate equation of the line represented by the following equation:
x2 - 4y2 = 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 x2 + kxy − 3y2 = 0 is equal to their product.
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 joint equation of the pair of lines through the origin and making an equilateral triangle with the line x = 3.
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 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
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.
Find k if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.
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 straight lines passing through origin and having slopes `(1 + sqrt2) and (1/(1 + sqrt2))` 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 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 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 ______.
Write the separate equations of lines represented by the equation 5x2 – 9y2 = 0
Write the joint equation of co-ordinate axes.
Find the combined equation of the pair of lines passing through the origin and perpendicular to the lines represented by 3x2 + 2xy – y2 = 0.
Combined equation of the lines bisecting the angles between the coordinate axes, is ______.
Find the joint equation of the pair of lines through the origin and perpendicular to the lines given by 2x2 + 7xy + 3y2 = 0
