`(8,3sqrt3)` is a point on the hyperbola `9x^(2) - 16y^(2) = 144.`

Show that the difference of the focal distances of any point on the hyperbola 9x^(2) - 16y^(2) = 144 is equal to its transverse axis.

Find the position of the point (7,2) with respect to the hyperbola 9x^(2) - 16y^(2) = 144 .

Find the length of the transverse and conjugate axes of the hyperbola 9x^(2) - 16y^(2) = 144 . Write down the equation of the hyperbola conjugate to it and find the eccentricities of both the hyperbolas.

Let P(4,3) be a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . If the normal at P intersects the x-axis at (16,0), then the eccentriclty of the hyperbola is

Find the parametric coordinates of the point ((1)/(sqrt(3)),(1)/(sqrt(2))) on the hyperbola 12x^(2) - 4y^(2) = 3

P is a veriable poin on the hyperbola x^(2) - y^(2) =16 and A (8,0) is a fixed point . Show that the locus of the middle point of the line segment bar(AP) is another rectangular hyperbola.

Find the locus of the-mid points of the chords of the circle x^2 + y^2=16 , which are tangent to the hyperbola 9x^2-16y^2= 144

If the coordinates of a point lies on the ellipse 9x^(2) + 16y^(2) = 144 be (2 , (3sqrt(3))/(2)) , find the eccentric angle of that point .

If the line 2x+sqrt(6)y=2 is a tangent to the hyperbola x^(2)-2y^(2)=4 , then the coordinates of the point of contact are -

The coordinates of the point on the ellipse 9x^(2) + 16y^(2) = 144 are (2,(3sqrt(3))/(2)) , find the eccentric angle of the point .