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
The equation represents
an ellipse
a parabola
a hyperbola
a circle
The equations of the transverse and conjugate axes of a hyperbola respectively are x + 2y - 3 = 0, 2x - y + 4 = 0 and their respective length are √2 and 2/√3. The equation of the hyperbola is.
2/5 ( x + 2y - 3)2 - 3/5 (2x - y + 4)2 = 1
2/5 (2x - y + 4)2 - 3/5 (x + 2y - 3)2 = 1
2 (2x - y + 4 )2 - 3 (x + 2y - 3)2 = 1
2 (x + 2y - 3)2 - 3 (2x - y + 4)2 = 1
The eccentricity of the hyperbola x2 - 4y2 = 1 is
√5/2
√3/2
2/√5
2/√3
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' are the eccentricities of hyperbolas and , then
e = e'
e = -e'
ee' = 1
1/e2 + 1/e'2 = 1
For a hyperbola, the foci are at (±4, 0) and vertices at (±2, 0).Its equation is
If m is a variable , the locus of the point of intersection of the lines and is
The eccentricity of the conic x2 - 2x - 4y2 = 0 is
1/4
3/2
√5/4
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