The equations of the transverse and conjugate axes of a hyperbola respectively are x + 2 y - 3 = 0, 2 x - y + 4 = 0 and their respective length are √2 and 2/√3. The equation of the hyperbola is.
2/5 ( x + 2 y - 3)2 - 3/5 (2 x - y + 4)2 = 1
2/5 (2 x - y + 4)2 - 3/5 (x + 2 y - 3)2 = 1
2 (2 x - y + 4 )2 - 3 (x + 2 y - 3)2 = 1
2 (x + 2 y - 3)2 - 3 (2 x - y + 4)2 = 1
Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = b2/a2
The equation of the chord of the hyperbola x2 - y2 = 9 which is bisected at (5, -3) is
5 x + 3 y = 9
5 x - 3 y = 16
5 x + 3 y = 16
5 x - 3 y = 9
The diameter of 16 x2 - 9 y2 = 144 which is conjugate to x = 2 y is
y = 16/9 x
y = 32/9 x
x = 16/9 y
x = 32/9 y
If m is a variable , the locus of the point of intersection of the lines and is
a parabola
an ellipse
a hyperbola
a circle
For a hyperbola, the foci are at (±4, 0) and vertices at (±2, 0).Its equation is
The eccentricity of the conic x2 - 2 x - 4 y2 = 0 is
1/4
3/2
√5/2
√5/4
The length of the latus rectum of the hyperbola is
2a2/b
2b2/a
b2/a
a2/b
The locus of the points of intersection of perpendicular tangents to is
x2 + y2 = a2 + b2
x2 - y2 = a2 - b2
x2 + y2 = a2 - b2
x2 - y2 = a2 + b2
If the chords of contact of tangents from two points (x1,y1) and (x2,y2) to the hyperbola are at right angles, then is equal to
-a2/b2
-b2/a2
-b4/a4
-a4/b4
