Advertisements
Advertisements
प्रश्न
. Show that the lines represented by 3x2 - 4xy - 3y2 = 0 are perpendicular to each other.
उत्तर
Comparing the equation 3x2 - 4xy - 3y2 = 0 with ax2 + 2hxy + by2 = 0, we get, a = 3, 2h = -4, b = -3.
Since a + b = 3 + (- 3) = 0, the lines represented by 3x2 - 4xy - 3y2 = 0 are perpendicular to each other.
APPEARS IN
संबंधित प्रश्न
Find the value of k if lines represented by kx2 + 4xy – 4y2 = 0 are perpendicular to each other.
Find the measure of the acute angle between the line represented by:
2x2 + 7xy + 3y2 = 0
Find the measure of the acute angle between the line represented by:
(a2 - 3b2)x2 + 8abxy + (b2 - 3a2)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 = ______.
Find the joint equation of the pair of lines which bisect angles between the lines given by x2 + 3xy + 2y2 = 0
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.
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.
The acute angle between the lines represented by x2 + xy = 0 is ______.
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 4ab = 3h2, then the ratio of slopes of the lines represented by the equation ax2 +2hxy + by2 = 0 will be ______
The acute angle between lines x - 3 = 0 and x + y = 19 is ______.
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)|`
Find the combined equation of the pair of lines through the origin and making an angle of 30° with the line 2x – y = 5
If θ is the acute angle between the lines given by 3x2 – 4xy + by2 = 0 and tan θ = `1/2`, find b.
The joint equation of the angle bisectors of the angles between the lines 4x2 – 16xy + 7y2 = 0 is ______.
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.
