Conic Section - Hyperbola by ednexa.com

1. Hyperbola
1. Equation of the tangent to the hyperbola
(x2/a2) – (y2/b2) =1
i. at P (x1,y1) is 1 1
2 2
xx yy
1
a b
 
ii. at P (θ) is x y
sec tan 1
a b
  
iii. in terms of slope m is y = mx 2 2 2
a m b  and
point of contact is
2 2
a m b
, .
c c
  
 
 
2. Equation of the normal to the hyperbola (x2/a2) –
(y2/b2) =1
i. at P (x1,y1) is
2 2
2 2
1 1
a x b y
a b
x y
  
ii. at P (θ) is 2 2ax by
a b .
sec tan
  
 
3. Equation of the director circle of the hyperbola is
x2+y2=a2-b2(a>b).
4. If the tangent at P on the hyperbola meets the
directrix in F, then PF subtends a right angle at the
corresponding focus.

2. 5. The tangents at the extremities of the latus
rectum of the hyperbola meets on the directrix of
the hyperbola.
6. The tangent at a point P on a hyperbole bisects
the angle between the focal radii of the point P.
7. The product of the lengths of perpendiculars from
the foci on any tangent to the hyperbola
2 2
2 2
x y
1
a b
  is
equal to b2.
For more study material visit www.ednexa.com
-Team Ednexa