Question

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

Solution

Correct option is

Auxiliary circle

Any tangent to hyperbola 

                  ….. (1)

Any line ⊥ to (1) is x + my = c                  ….. (2)

(2) Passes through S(ae, 0) ∴ C = ae.

Now (2) ⇒ x + my = ae

The locus of k, the feet of perpendicular is obtained …. (3)

By eliminating m between (1) & (3). Square & add (1) and (3).

⇒ x2 + y2 = a2 which is auxiliary circle.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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Q7

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

Q8

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

Q9

The line 3x + 2y + 1 = 0 meets the hyperbola 4x2 – y2 = 4a2 in the points P and Q. The coordinates of point intersection of the tangents at and Qare

Q10

The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is