Advertisements
Advertisements
प्रश्न
If ax2 + 2hxy + by2 = 0 represents a pair of lines and h2 = ab ≠ 0 then find the ratio of their slopes.
उत्तर
h2 = ab
∴ h2 − ab = 0
∴ Lines are real and coincident.
Let m1 and m2 be the slope of lines represented by the equation ax2 + 2hxy + by2 = 0.
As the lines are real and coincident,
∴ m1 = m2
∴ `"m"_1/"m"_2` = 1
Their ratio is 1 : 1.
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 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 `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 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.
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.
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.
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
Find the value of h, if the measure of the angle between the lines 3x2 + 2hxy + 2y2 = 0 is 45°.
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 = ______
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?
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.
