Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
6(x – 1)2 + 5( x – 1)(y – 2) – 4(y – 3)2 = 0
Let x = x – 1 and y = y – 2
∴ The given equation becomes
6x2 + 5xy – 4y2 = 0
6x2 + 8xy – 3xy – 4y2 = 0
2x(3x + 4y) – Y(3x + 4y) = 0
(2x – y)(3x + 4y) = 0
2x – y = 0 and 3x + 4y = 0
Substituting for x and y, we have
2x – y = 0
⇒ 2(x – 1) – (y – 2) = 0
⇒ 2x – 2 – y + 2 = 0
⇒ 2x – y = 0
3X + 4Y = 0
⇒ 3(x – 1) + 4( y – 2 ) = 0
⇒ 3x – 3 + 4y – 8 = 0
⇒ 3x + 4y – 11 = 0
∴ The separate equations are
2x – y = 0 and 3x + 4y – 11 = 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.
Show that the pair of straight lines 4x2 + 12xy + 9y2 – 6x – 9y + 2 = 0 represents two parallel 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:
Combined equation of co-ordinate axes is:
Find the combined equation of the straight lines whose separate equations are x − 2y − 3 = 0 and x + y + 5 = 0
Show that 2x2 + 3xy − 2y2 + 3x + y + 1 = 0 represents a pair of perpendicular lines
The slope of one of the straight lines ax2 + 2hxy + by2 = 0 is twice that of the other, show that 8h2 = 9ab
A ∆OPQ is formed by the pair of straight lines x2 – 4xy + y2 = 0 and the line PQ. The equation of PQ is x + y – 2 = 0, Find the equation of the median of the triangle ∆ OPQ drawn from the origin O
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
Show that the equation 4x2 + 4xy + y2 – 6x – 3y – 4 = 0 represents a pair of parallel lines. Find the distance between them
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.
Choose the correct alternative:
The area of the triangle formed by the lines x2 – 4y2 = 0 and x = a is
Choose the correct alternative:
One of the equation of the lines given by x2 + 2xy cot θ – y2 = 0 is
The pair of lines represented by 3ax2 + 5xy + (a2 – 2)y2 = 0 are perpendicular to each other for ______.
