If 2x−y+1=0 is a tangent to the hyperbola a2x2−16y2=1 then which of the following CANNOT be sides of a right angled triangle? (a)a,4,2 (b) a,4,1(c)2a,4,1 (d) 2a,8,1
A hyperbola passes through (2,3) and has asymptotes 3x−4y+5=0 and 12x+5y−40=0 . Then, the equation of its transverse axis is 77x−21y−265=0 21x−77y+265=0 21x−77y−265=0 21x+77y−265=0
Two tangents to the hyperbola a2x2−b2y2=1 having m1andm2 cut the axes at four concyclic points. Fid the value of m1m2˙
If the base of a triangle and the ratio of tangent of half of base angles are given, then identify the locus of the opposite vertex.
The tangent at a point P on the hyperbola a2x2−b2y2=1 meets one of the directrix at F˙ If PF subtends an angle θ at the corresponding focus, then θ= 4π (b) 2π (c) 43π (d) π
Show that the equation 9x2−16y2−18x+32y−151=0 represents a hyperbola. Find the coordinates of the centre, lengths of the axes, eccentricity, latus-rectum, coordinates of foci and vertices, equations of the directrices of the hyperbola.