Advertisements
Advertisements
प्रश्न
If the slope of one of the two lines given by `"x"^2/"a" + "2xy"/"h" + "y"^2/"b" = 0` is twice that of the other, then ab : h2 = ______.
विकल्प
1 : 2
2 : 1
8 : 9
9 : 8
Advertisements
उत्तर
If the slope of one of the two lines given by `"x"^2/"a" + "2xy"/"h" + "y"^2/"b" = 0` is twice that of the other, then ab : h2 = 9 : 8.
Explanation:
ax2 + 2hxy + by2 =0
m1 + m2 = `(-2"h")/"b"` and m1m2 = `"a"/"b"`
where m1 = Km2
Km1 + m2 = `(-2"h")/"b"`
m2(K+1) =`(-2h)/(b)`
m2 = `(-2h)/(b(K+1))`
Km2m2 = `a/b`
`"K" "m"_2^2 = a/b`
`"K" ((-2h)/(b(K+1)))^2 = a/b`
`K (4h^2)/(b^2(K+1)^2) = a/b`
`4Kh^2 = (K+1)^2ab`
`4(2)(1/h)^2 = 9 1/a 1/b`
`8/h^2 =9/(ab)`
`(ab)/h^2=9/8`
APPEARS IN
संबंधित प्रश्न
Find the combined equation of the following pair of lines:
2x + y = 0 and 3x − y = 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:
3y2 + 7xy = 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 separate equation of the line represented by the following equation:
x2 + 2(cosec α)xy + 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:
3x2 − 4xy = 0
Choose correct alternatives:
Auxiliary equation of 2x2 + 3xy - 9y2 = 0 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 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.
Find the joint equation of the line passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18
Show that the following equations represents a pair of line:
x2 + 2xy - y2 = 0
Show that the following equations represent a pair of line:
x2 - y2 = 0
Show that the following equations represent a pair of line:
x2 + 7xy - 2y2 = 0
Show that the following equations represent a pair of line:
`"x"^2 - 2sqrt3"xy" - "y"^2 = 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 one of the lines given by 3x2 - kxy + 5y2 = 0 is perpendicular to the line 5x + 3y = 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.
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 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.
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 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 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 ______.
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 y-axis and the line through the origin having slope 3.
The distance between the lines represented by the equation 4x² + 4xy + y² − 6x − 3y − 4 = 0 is
