" (iv) "(1)/(16x^(2)-9a^(2))

Find the co-ordinates of the vertices, the foci, the eccentricity and the length of latus-rectum of the hyperbolas : (a) (x^(2))/(9) -(y^(2))/(16) = 1 (b) (i) 16x^(2) - 9y^(2) = 576 (ii) y^(2) -16x^(2) = 1 (iii) 5y^(2) - 9x^(2) = 36 (iv) 49y^(2) - 16x^(2) = 784 .

(64x^(3)-:27backslash a^(-3))^(-2/3)= a.(9ax)/(16) b.(9)/(16ax) c.(9)/(16x^(2)a^(2)) d.(3)/(4)x^(-2)a^(-2)

Find the equation of normals of the following curves at the given points: (i) Curve y^(2)=4 ax" at point "(at^(2), 2at) . (ii) Curve y= e^(x)" at point "(0, 1) (iii) Curve y = x^(3)" at point "(1, 1) . (iv) Curve 2y = 3 - x^(2)" at point "(1, 1) . (v) Curve 16x^(2)-9y^(2) = 432 at point (6, 4).

The partial fractions of (1)/((x^(2)+9)(x^(2)+16)) are

(4x^(2)-11x+6)/(16x^(2)-9)

Equation of the hyperbola with foci (0,pm5) and e=(5)/(3) is (1) (x^(2))/(9)-(y^(2))/(16)=1 (2) (x^(2))/(16)-(y^(2))/(9)=-1 (3) (x^(2))/(16)-(y^(2))/(9)=1 (4) (x^(2))/(12)-(y^(2))/(13)=1