Question

The normal to the rectangular hyperbola xy = c2 at the point ‘t’ meets the curve again at point “t” such that

Solution

Correct option is

t3t’ = –1

Any point P on xy = c2         ….. (1)  

Similarly another point Q is . Diff. (1) w.r.t. x,

        

So equation of normal at P is

       

⇒ t3x – ty + (c – ct4) = 0                          …. (2)

Equation of line PQ is y – y1

                             

Now (2) and (3) represent same line

⇒ x + ytt’ – c(t + t’) = 0                       …. (3)

⇒ t3t’ = –1

SIMILAR QUESTIONS

Q1

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

Q2

The ,locus of the middle points of portions of the tangents to the hyperbola , intercepted between the axes is

Q3

If the polar of a point with respect to  toches the hyperbola , then the locus of the point is

Q4

The locus of pole of any tangent to the circle x2 + y2 = 4 w.r.t. the hyperbola x2 – y= 4 is the circle

Q5

The foci of a hyperbola coincide with the foci of the ellipse . The equation of the hyperbola if its eccentricity is 2, is

Q6

PN is the ordinate of any point P on the hyperbola  and AA’ is its transverse axis. If Q divides AP in the ratio a2 : b2, then NQ is

Q7

If SK perpendicular from focus S on th tangent at any point P of the hyperbola  , then K lies on

Q8

The lines 2x + 3y + 4 = 0 and 3x – 2y + 5 = 0 may be conjugate w.r.t. the hyperbola  if

Q9

The condition for two diameters of a hyperbola  represented by Ax2 + 2Hxy + By2 = 0 to be conjugate is

Q10

If the polars of (x1y1) and (x2y2) w.r.t. the hyperbola  are at right angles, then