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
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 the normal at (ct, c/t) on the curve xy = c2 meets the curve again in 't' , then
t' = -1/t3
t' = -1/t
t' = 1/t2
t'2 = -1/t2
If e, e' are the eccentricities of hyperbolas and , then
e = e'
e = -e'
ee' = 1
1/e2 + 1/e'2 = 1
The line y = 4x + c touches the hyperbola x2 - y2 = 1 iff
c = 0
c = ± √2
c = ± √15
c = ± √17
P is a point on the hyperbola , N is the foot of the⊥ from P on the transverse axis.The tangent to the hyperbola at P meets the transverse axis at T.If O is the centre of the hyperbola, then OT.ON is equal to
e2
a2
b2
b2/a2
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 equation represents
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
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
