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
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
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 e and e1 are the eccentricities of the hyperbolas xy = c2 and x2 - y2 = c2 , then e2 + e21 is equal to
1
4
6
8
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
The equation represents
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 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
