Advertisements
Advertisements
प्रश्न
Find the separate equation of the line represented by the following equation:
x2 + 2(cosec α)xy + y2 = 0
Advertisements
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:
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 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:
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
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:
If two lines ax2 + 2hxy + by2 = 0 make angles α and β with X-axis, then tan (α + β) = _____.
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 ______.
Choose correct alternatives:
The combined equation of the coordinate axes is
Choose correct alternatives:
If slope of one of the lines ax2 + 2hxy + by2 = 0 is 5 times the slope of the other, then 5h2 = ______
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 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.
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:
x2 - y2 = 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:
x2 - 4y2 = 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 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 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.
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
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.
Find the joint equation of the line passing through the origin and having slopes 1 + `sqrt3` and 1 - `sqrt3`
The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis 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 pair of lines having slopes `1+sqrt2` and `1-sqrt2` and passing through the origin 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
