Advertisements
Advertisements
प्रश्न
Show that 2x2 + 3xy − 2y2 + 3x + y + 1 = 0 represents a pair of perpendicular lines
उत्तर
Comparing the given equation with the general form a = 2
h = `3/2`
b = – 2
g = `3/2`
f = `1/2`
c = 1
Condition for two lines to be perpendicular is a + b = 0.
Here a + b
= 2 – 2
= 0
⇒ The given equation represents a pair of perpendicular lines.
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.
Show that the equation 12x2 – 10xy + 2y2 + 14x – 5y + 2 = 0 represents a pair of straight lines and also find the separate equations of the straight lines.
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:
The angle between the pair of straight lines x2 – 7xy + 4y2 = 0 is:
Find the separate equation of the following pair of straight lines
6(x – 1)2 + 5(x – 1)(y – 2) – 4(y – 3)2 = 0
The slope of one of the straight lines ax2 + 2hxy + by2 = 0 is three times the other, show that 3h2 = 4ab
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
For what values of k does the equation 12x2 + 2kxy + 2y2 +11x – 5y + 2 = 0 represent two straight lines
Show that the equation 9x2 – 24xy + 16y2 – 12x + 16y – 12 = 0 represents a pair of parallel lines. Find the distance between them
Prove that one of the straight lines given by ax2 + 2hxy + by2 = 0 will bisect the angle between the coordinate axes if (a + b)2 = 4h2
If the pair of straight lines x2 – 2kxy – y2 = 0 bisect the angle between the pair of straight lines x2 – 2lxy – y2 = 0, Show that the later pair also bisects the angle between the former
Choose the correct alternative:
The length of ⊥ from the origin to the line `x/3 - y/4` = 1 is
Choose the correct alternative:
The area of the triangle formed by the lines x2 – 4y2 = 0 and x = a is
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 ______.
