Advertisements
Advertisements
प्रश्न
Find the separate equation of the line represented by the following equation:
x2 + 2(cosec α)xy + y2 = 0
उत्तर
x2 + 2(cosec α)xy + y2 = 0
i.e. y2 + 2(cosec α)xy + x2 = 0
Dividing by x2, we get,
`("y"/"x")^2 + 2"cosec"alpha. ("y"/"x") + 1 = 0`
`therefore "y"/"x" = (-2 "cosec" alpha +- sqrt(4"cosec"^2 alpha - 4 xx 1 xx 1))/(2xx1)`
`= (-2 "cosec" alpha +- 2sqrt("cosec"^2 alpha - 1))/2`
= - cosec α ± cot α
`therefore "y"/"x" = ("cot" alpha - "cosec" alpha)` and
`"y"/"x" = - ("cosec" alpha + "cot" alpha)`
The separate equations of the lines are
(cosec α - cot α) x + y = 0 and (cosec α + cot α) x + y = 0
Notes
Answer in the textbook is incorrect.
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 line:
x + 2y - 1 = 0 and x - 3y + 2 = 0
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 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:
3x2 - 4xy = 0
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 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:
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.
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 3x2 + kxy - y2 = 0 is zero.
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.
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 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
Find the condition that the equation ay2 + bxy + ex + dy = 0 may represent a pair of lines.
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.
If equation ax2 - y2 + 2y + c = 1 represents a pair of perpendicular lines, then find a and c.
Find the joint equation of the line passing through the origin and having slopes 1 + `sqrt3` and 1 - `sqrt3`
The combined equation of the lines through origin and perpendicular to the pair of lines 3x2 + 4xy − 5y2 = 0 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 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
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.
