A hyperbola passes through the point P(2,3)and has foci at (±2,0)˙Then the tangent to this hyperbola at Palso passes through the point :
A point P moves such that the chord of contact of the pair of tangents from P on the parabola y2=4ax touches the rectangular hyperbola x2−y2=c2˙ Show that the locus of P is the ellipse c2x2+(2a)2y2=1.
If any line perpendicular to the transverse axis cuts the hyperbola a2x2−b2y2=1 and the conjugate hyperbola a2x2−b2y2=−1 at points PandQ , respectively, then prove that normal at PandQ meet on the x-axis.
A hyperbola is given with its vertices at (−2,0) and (2,0) one of the foci of hyperbola is (3,0). Then which of the following points does not lie on hyperbola (A) (24,5) (B) (44,52) (C) (44,−52) (D) (−6,52)
OA and OB are fixed straight lines, P is any point and PM and PN are the perpendiculars from P on OAandOB, respectively. Find the locus of P if the quadrilateral OMPN is of constant area.
A tangent drawn to hyperbola a2x2−b2y2=1at P(6π) forms a triangle of area 3a2 square units, with coordinate axes, then the squae of its eccentricity is equal to
Find the locus of the point of intersection of the lines 3x−y−43λ=0and3λx+λy−43=0 for different values of λ˙