If the hyperbola `x^2-y^2=4` is rotated by `45^0` in the anticlockwise direction about its center keeping the axis intact, then the equation of the hyperbola is `x y=a^2,` where `a^2` is equal to___________

The vertices of the hyperbola 9x^2 - 16y^2 = 144

Find the equation of normal to the hyperbola x^2-9y^2=7 at point (4, 1).

Find the equation of normal to the hyperbola x^2-9y^2=7 at point (4, 1).

If the pair of lines sqrt(3)x^2-4x y+sqrt(3)y^2=0 is rotated about the origin by pi/6 in the anticlockwise sense, then find the equation of the pair in the new position.

Find the vertices of the hyperbola 9x^2-16 y^2-36 x+96 y-252=0

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal to that of the ellipse x^2+4y^2=4. if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+9y^2+14 x+22 y+7=0

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+8y^2+14 x+22 y+7=0