Advertisements
Advertisements
प्रश्न
Find the angle between the pair of straight lines 3x2 – 5xy – 2y2 + 17x + y + 10 = 0.
Advertisements
उत्तर
The given equation is 3x2 – 5xy – 2y2 + 17x + y + 10 = 0
Here a = 3, 2h = -5, b = -2
If θ is the angle between the given straight lines then
θ = `tan^-1 [|(2sqrt("h"^2 - ab))/(a + b)|]`
`= tan^-1 [(2sqrt(((-5)/2)^2 - 3(-2)))/(3 + (- 2))]`
`= tan^-1 [|(2sqrt(25/4 + 6))/1|]`
`= tan^-1 [|2 sqrt((25 + 24)/4)|]`
`= tan^-1 [|2 xx sqrt(49/4)|]`
`= tan^-1 [|2xx7/2|]`
= tan-1 (7)
APPEARS IN
संबंधित प्रश्न
If the equation ax2 + 5xy – 6y2 + 12x + 5y + c = 0 represents a pair of perpendicular straight lines, find a and c.
If m1 and m2 are the slopes of the pair of lines given by ax2 + 2hxy + by2 = 0, then the value of m1 + m2 is:
If the lines 2x – 3y – 5 = 0 and 3x – 4y – 7 = 0 are the diameters of a circle, then its centre is:
ax2 + 4xy + 2y2 = 0 represents a pair of parallel lines then ‘a’ is:
Show that 4x2 + 4xy + y2 − 6x − 3y − 4 = 0 represents a pair of parallel lines
Find p and q, if the following equation represents a pair of perpendicular lines
6x2 + 5xy – py2 + 7x + qy – 5 = 0
Find the value of k, if the following equation represents a pair of straight lines. Further, find whether these lines are parallel or intersecting, 12x2 + 7xy − 12y2 − x + 7y + k = 0
Prove that the straight lines joining the origin to the points of intersection of 3x2 + 5xy – 3y2 + 2x + 3y = 0 and 3x – 2y – 1 = 0 are at right angles.
The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A'B (where B is the point (2, 3)) subtend angle `π/4` at the origin, is equal to ______.
Let the equation of the pair of lines, y = px and y = qx, can be written as (y – px) (y – qx) = 0. Then the equation of the pair of the angle bisectors of the lines x2 – 4xy – 5y2 = 0 is ______.
