Advertisements
Advertisements
प्रश्न
Find the separate equation of the following pair of straight lines
3x2 + 2xy – y2 = 0
Advertisements
उत्तर
Factorising 3x2 + 2xy – y2 we get
3x2 + 3xy – xy – y2 = 3x(x + y) – y(x + y)
= (3x – y)(x + y)
So 3x2 + 2xy – y2 = 0
⇒ (3x – y)(x + y) = 0
⇒ 3x – y = 0 and x + y = 0
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.
Find the angle between the pair of straight lines 3x2 – 5xy – 2y2 + 17x + y + 10 = 0.
If the lines 2x – 3y – 5 = 0 and 3x – 4y – 7 = 0 are the diameters of a circle, then its centre is:
Combined equation of co-ordinate axes is:
Show that 4x2 + 4xy + y2 − 6x − 3y − 4 = 0 represents a pair of parallel lines
Show that 2x2 + 3xy − 2y2 + 3x + y + 1 = 0 represents a pair of perpendicular lines
Prove that the equation to the straight lines through the origin, each of which makes an angle α with the straight line y = x is x2 – 2xy sec 2α + y2 = 0
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
Find the separate equation of the following pair of straight lines
2x2 – xy – 3y2 – 6x + 19y – 20 = 0
The slope of one of the straight lines ax2 + 2hxy + by2 = 0 is three times the other, show that 3h2 = 4ab
Show that the equation 4x2 + 4xy + y2 – 6x – 3y – 4 = 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
Choose the correct alternative:
The image of the point (2, 3) in the line y = −x is
Choose the correct alternative:
If one of the lines given by 6x2 – xy – 4cy2 = 0 is 3x + 4y = 0, then c equals to ______.
Choose the correct alternative:
One of the equation of the lines given by x2 + 2xy cot θ – y2 = 0 is
If `"z"^2/(("z" - 1))` is always real, then z, can lie on ______.
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 ______.
