The length of the transverse axis of the rectangular hyperbola `x y=18` is 6 (b) 12 (c) 18 (d) 9

The length of the transverse axis of the hyperbola 9x^(2)-16y^(2)-18x -32y - 151 = 0 is

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

The equation of the transvers axis of the hyperbola (x-3)^2+(y=1)^2+(4x+3y)^2 is x+3y=0 (b) 4x+3y=9 3x-4y=13 (d) 4x+3y=0

If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these

The equation of conjugate axis of the hyperbola x y-3y-4x+7=0 is (a) y+x=3 (b) y+x=7 (c) y-x=3 (d) none of these

At the point of intersection of the rectangular hyperbola xy=c^2 and the parabola y^2=4ax tangents to the rectangular hyperbola and the parabola make angles theta and phi , respectively with x-axis, then

The equation 16 x^2-3y^2-32 x+12 y-44=0 represents a hyperbola. the length of whose transvers axis is 4sqrt(3) the length of whose transvers axis is 4 whose center is (-1,2) whose eccentricity is sqrt((19)/3)

Find the eccetricity of hyperbola through (4,2) whose centre is (0.0) length of transverse axis is 4 and transverse axis along x-axis. (a) 2 (b) sqrt3 (c) (sqrt3)/(2) (d) (2)/(sqrt3)

The curve in the first quadrant for which the normal at any point (x , y) and the line joining the origin to that point form an isosceles triangle with the x-axis as base is (a) an ellipse (b) a rectangular hyperbola (c) a circle (d) None of these

The chord P Q of the rectangular hyperbola x y=a^2 meets the axis of x at A ; C is the midpoint of P Q ; and O is the origin. Then A C O is equilateral (b) isosceles right-angled (d) right isosceles