Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus rectum of the hyperbola 16x2−9y2=144
If the distance between the foci and the distance between the two directricies of the hyperbola a2x2−b2y2=1 are in the ratio 3:2, then b:a is (a)1:2 (b) 3:2 (c)1:2 (d) 2:1
From the center C of hyperbola a2x2−b2y2=1 , perpendicular CN is drawn on any tangent to it at the point P(asecθ,btanθ) in the first quadrant. Find the value of θ so that the area of CPN is maximum.
If tangents drawn from the point (a,2) to the hyperbola 16x2−9y2=1 are perpendicular, then the value of a2 is _____
The equation of conjugate axis of the hyperbola xy−3y−4x+7=0 is y+x=3 (b) y+x=7 y−x=3 (d) none of these
The equation of one of the directrices of a hyperboda is 2x+y=1, the corresponding focus is (1, 2) and e=3 . Find the equation of the hyperbola and the coordinates of the center and the second focus.
A variable line y=mx−1 cuts the lines x=2y and y=−2x at points AandB . Prove that the locus of the centroid of triangle OAB(O being the origin) is a hyperbola passing through the origin.
If two distinct tangents can be drawn from the Point (α,2) on different branches of the hyperbola 9x2−16y2=1 then (1) ∣α∣<23 (2) ∣α∣>32 (3)∣α∣>3 (4) α=1