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.
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:
If the lines 2x – 3y – 5 = 0 and 3x – 4y – 7 = 0 are the diameters of a circle, then its centre is:
Find the combined equation of the straight lines whose separate equations are x − 2y − 3 = 0 and x + y + 5 = 0
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
Show that the equation 2x2 − xy − 3y2 − 6x + 19y − 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is tan−1(5)
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
2x2 – xy – 3y2 – 6x + 19y – 20 = 0
Show that the equation 4x2 + 4xy + y2 – 6x – 3y – 4 = 0 represents a pair of parallel lines. Find the distance between them
Choose the correct alternative:
The coordinates of the four vertices of a quadrilateral are (−2, 4), (−1, 2), (1, 2) and (2, 4) taken in order. The equation of the line passing through the vertex (−1, 2) and dividing the quadrilateral in the equal areas is
Choose the correct alternative:
If the equation of the base opposite to the vertex (2, 3) of an equilateral triangle is x + y = 2, then the length of a side is
Choose the correct alternative:
The area of the triangle formed by the lines x2 – 4y2 = 0 and x = a 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
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 ______.
