For a hyperbola, the foci are at (±4, 0) and vertices at (±2, 0).Its equation is
The line y = 4x + c touches the hyperbola x2 - y2 = 1 iff
c = 0
c = ± √2
c = ± √15
c = ± √17
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
A rectangular hyperbola is one in which
the two axes are rectangular
the two axes are equal
the asymptotes are perpendicular
the two branches are perpendicular
If e,e' be the eccentricities of two conics S and S' and if e2 + e'2 = 3, then both S and S' can be
Ellipses
Parabola
Hyperbolas
None of these
If e, e' are the eccentricities of hyperbolas and , then
e = e'
e = -e'
ee' = 1
1/e2 + 1/e'2 = 1
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 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
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
Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = b2/a2
