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प्रश्न
The acute angle between the lines represented by x2 + xy = 0 is ______.
विकल्प
`pi/2`
`pi/4`
`pi/6`
`pi/3`
उत्तर
The acute angle between the lines represented by x2 + xy = 0 is `underlinebb(pi/4)`.
APPEARS IN
संबंधित प्रश्न
. Show that the lines represented by 3x2 - 4xy - 3y2 = 0 are perpendicular to each other.
Show that the lines represented by x2 + 6xy + 9y2 = 0 are coincident.
Find the measure of the acute angle between the line represented by `3"x"^2 - 4sqrt3"xy" + 3"y"^2 = 0`
Find the measure of the acute angle between the line represented by:
4x2 + 5xy + y2 = 0
Find the combined equation of lines passing through the origin each of which making an angle of 30° with the line 3x + 2y - 11 = 0
Find the combined equation of lines passing through the origin and each of which making an angle of 60° with the Y-axis.
Choose correct alternatives:
If acute angle between lines ax2 + 2hxy + by2 = 0 is, `pi/4`, then 4h2 = ______.
Show that the lines x2 − 4xy + y2 = 0 and x + y = 10 contain the sides of an equilateral triangle. Find the area of the triangle.
If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is three times the other, prove that 3h2 = 4ab.
Show that the line 3x + 4y + 5 = 0 and the lines (3x + 4y)2 - 3(4x - 3y)2 = 0 form the sides of an equilateral triangle.
Show that the lines x2 - 4xy + y2 = 0 and the line x + y = `sqrt6` form an equilateral triangle. Find its area and perimeter.
If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is square of the slope of the other line, show that a2b + ab2 + 8h3 = 6abh.
Prove that the product of length of perpendiculars drawn from P(x1, y1) to the lines represented by ax2 + 2hxy + by2 = 0 is `|("ax"_1^2 + "2hx"_1"y"_1 + "by"_1^2)/(sqrt("a - b")^2 + "4h"^2)|`
Show that the difference between the slopes of the lines given by (tan2θ + cos2θ)x2 - 2xy tan θ + (sin2θ)y2 = 0 is two.
Find the measure of the acute angle between the lines given by x2 − 4xy + y2 = 0
If θ is the acute angle between the lines given by ax2 + 2hxy + by2 = 0 then prove that tan θ = `|(2sqrt("h"^2) - "ab")/("a" + "b")|`. Hence find acute angle between the lines 2x2 + 7xy + 3y2 = 0
If the angle between the lines represented by ax2 + 2hxy + by2 = 0 is equal to the angle between the lines 2x2 − 5xy + 3y2 = 0, then show that 100(h2 − ab) = (a + b)2
The angle between the pair of straight lines 2x2 - 6xy + y2 = 0 is tan-1 (p), where p = ______
The angle between lines `(x - 2)/2 = (y - 3)/(- 2) = (z - 5)/1` and `(x - 2)/1 = (y - 3)/2 = (z - 5)/2` is ______.
If 4ab = 3h2, then the ratio of slopes of the lines represented by the equation ax2 +2hxy + by2 = 0 will be ______
Which of the following pair of straight lines intersect at right angles?
The acute angle between the curve x = 2y2 and y = 2x2 at `(1/2, 1/2)` is ______.
If slopes of lines represented by kx2 + 5xy + y2 = 0 differ by 1, then k = ______.
If θ is the acute angle between the lines represented by ax2 + 2hxy + by2 = 0 then prove that tan θ = `|(2sqrt(h^2 - ab))/(a + b)|`
If the lines represented by 5x2 – 3xy + ky2 = 0 are perpendicular to each other, find the value of k.
Prove that the acute angle θ between the lines represented by the equation ax2 + 2hxy+ by2 = 0 is tanθ = `|(2sqrt(h^2 - ab))/(a + b)|` Hence find the condition that the lines are coincident.
