Straight LineHard
Question
If the straight lines joining the origin and the points of intersection of the curve 5x2 + 12xy - 6y2 + 4x - 2y + 3 = 0 and x + ky - 1 = 0 are equally inclined to the co-ordi nate axis, then the value of k -
Options
A.is equal to 1
B.is equal to -
C.is equal to 2
D.does not exist in the set of real numbers
Solution
Homogenizing the curve with the help of the straight line.
5x2 + 12xy - 6y2 + 4x(x + ky) - 2y (x + ky) + 3(x + ky)2 = 0
12x2 + (10 + 4k + 6k) xy + (3k2 -2k - 6)y2 = 0
Lines are equally inclined to the coordinate axes
⇒ coefficient of xy = 0
⇒ 10k + 10 = 0 ⇒ k = - 1
5x2 + 12xy - 6y2 + 4x(x + ky) - 2y (x + ky) + 3(x + ky)2 = 0
12x2 + (10 + 4k + 6k) xy + (3k2 -2k - 6)y2 = 0
Lines are equally inclined to the coordinate axes
⇒ coefficient of xy = 0
⇒ 10k + 10 = 0 ⇒ k = - 1
Create a free account to view solution
View Solution FreeMore Straight Line Questions
Number of straight lines from (1, 1) which make area of 1 sq. units with the coordinate axes is equal to -...The foot of the perpendicular drawn from the point (7, 8) to the line 2x + 3y − 4 = 0 is -...The equation of the lines which pass through theorigin and are inclined at an angle tan-1 m to theline y = mx + c, are -...If a ray traveling along the line x = 1 gets reflected from the line x + y = 1 then the equation of the line along which...A variable line passes through a fixed point (a, b) and meets the co-ordinates axes in A and B. The locus of the point o...