Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = b2/a2
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 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
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
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
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
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
For a hyperbola, the foci are at (±4, 0) and vertices at (±2, 0).Its equation is
