HyperbolaHard
Question
The locus of the point of intersection of the lines √3x - y - 4 √3k = 0 and √3kx + ky - 4 √3 = 0 for different values of k is -
Options
A.ellipse
B.parabola
C.circle
D.hyperbola
Solution
Let point of intersection is (x1, y1).
So. √3 x1 - y1 = 4 √3 K ... (i)
√3 K x1 + Ky1 = 4 √3 ... (ii)
Multiply (i) and (ii), we get 3x12 - y12 = 48.
So. √3 x1 - y1 = 4 √3 K ... (i)
√3 K x1 + Ky1 = 4 √3 ... (ii)
Multiply (i) and (ii), we get 3x12 - y12 = 48.
Create a free account to view solution
View Solution FreeMore Hyperbola Questions
The equations to the common tangents to the two hyperbolas = 1 and = 1 are-...If the line $\alpha x + 2y = 1$, where $\alpha \in \mathbb{R}$, does not meet the hyperbola $x^{2} - 9y^{2} = 9$, then a...The locus of the point of intersection of the lines bxt − ayt = ab and bx + ay = abt is −...The tangents to the hyperbola x2 − y2 = 3 are parallel to the straight line 2x + y + 8 = 0 at the following points...Let PQ be a chord of the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{{\text{ }b}^{2}} = 1$, perpendicular to the x -axis s...