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
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