Question

The condition that the straight line lx + my = n may be a normal to the hyperbola b2x2 – a2y2 = a2b2 is

Solution

Correct option is

 

lx + my = n  … (1) is normal to hyperbola

  b2x2 – a2y2 = a2b2             ….. (2) by (2)

                       …. (3)

Normal at any point P  is

             

Compare (1) and (4),

          

         

SIMILAR QUESTIONS

Q1

 

The curve for which the slope of the tangent at any point equals the ratio of the abscissa to the ordinate of the point is

 

Q2

 

The line P = x  become tangent to  if

 

Q3

The product of perpendicular drawn from any point on the hyperbola to its asymptotes is

Q4

 

The locus of the point of intersection of the lines 

, where m is a parameter, is always

Q5

If the eccentricities of the hyperbolas  and  be eand e1, then 

Q6

 

The locus rectum of the hyperbola

9x2 – 16y2 – 18x – 32y – 151 = 0 is

Q7

The eccentricity of the conjugate hyperbola of the hyperbola x2 – 3y2 = 1 is

Q8

The distance between the directrices of a rectangular hyperbola is 10 units, then distance between its foci is