Three points A,B and C taken on rectangular hyperbola xy=4 where B(−2,−2) and C(6,2/3). The normal at A is parallel to BC, then
The lines parallel to the normal to the curve xy=1 is/are 3x+4y+5=0 (b) 3x−4y+5=0 4x+3y+5=0 (d) 3y−4x+5=0
If the tangents to the parabola y2=4ax intersect the hyperbola a2x2−b2y2=1 at AandB , then find the locus of the point of intersection of the tangents at AandB˙
An ellipse intersects the hyperbola 2x2−2y=1 orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (b) the foci of ellipse are (±1,0) (a) equation of ellipse is x2+2y2=2 (d) the foci of ellipse are (t2,0) (c) equation of ellipse is (x22y)
PQ and RS are two perpendicular chords of the rectangular hyperbola xy=c2˙ If C is the center of the rectangular hyperbola, then find the value of product of the slopes of CP,CQ,CR, and CS˙
The curve xy=c,(c>0), and the circle x2+y2=1 touch at two points. Then the distance between the point of contacts is 1 (b) 2 (c) 22 (d) none of these
Find the lengths of the transvers and the conjugate axis, eccentricity, the coordinates of foci, vertices, the lengths of latus racta, and the equations of the directrices of the following hyperbola: 16x2−9y2=−144.
The locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse a2x2+b2y2=1 forms a triangle of constant area with the coordinate axes is a straight line (b) a hyperbola an ellipse (d) a circle