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 e ane e1 are the eccentricities of the hyperbolas xy = c2 and x2 - y2 = c2 , then e2 + e2 is equal to
1
4
6
8
Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = b2/a2
The equation represents
an ellipse
a parabola
a hyperbola
a circle
If m is a variable , the locus of the point of intersection of the lines and is
The eccentricity of the hyperbola x2 - 4y2 = 1 is
√5/2
√3/2
2/√5
2/√3
For the ellipse , the foci are
(± 1, 0)
(0, ± 1)
(± 1/√2, 0)
(± 1/2 , 0)
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
The line y = 2x + c touches the ellipse if c is equal to
0
± 2 √17
c = ± √15
c = ± √17
The equation ax2 + 2 hxy + by2 + 2 gx + 2 fy + c = 0 represents an ellipse if
Δ =0, h2 < ab
Δ ≠ 0, h2 < ab
Δ ≠ 0, h2 > ab
Δ ≠ 0, h2 = ab
