Let `P_i` and `P_i '` be the feet of the perpendiculars drawn from the foci `Sa n dS '` on a tangent `T_i` to an ellipse whose length of semi-major axis is 20. If `sum_(i=0)^(10)(S P_i)(S^(prime)Pi ')=2560 ,` then the value of eccentricity is (a) `1/5` (b) `2/5` (c) `3/5` (d) `4/5`

The value of sin^(-1)(cos(33pi)/5) is (a) (3pi)/5 (b) -pi/(10) (c) pi/(10) (d) (7pi)/5

Let d_1a n dd_2 be the length of the perpendiculars drawn from the foci Sa n dS ' of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 to the tangent at any point P on the ellipse. Then, S P : S^(prime)P= d_1: d_2 (b) d_2: d_1 d1 2:d2 2 (d) sqrt(d_1):sqrt(d_2)

If (0, 3+sqrt5) is a point on the ellipse whose foci and (2, 3) and (-2, 3) , then the length of the semi - major axis is

The value of sin^(-1)(cos((33pi)/5)) is (a) (3pi)/5 (b) -pi/(10) (c) pi/(10) (d) (7pi)/5

The argument of the complex number (i/2-2/i) is equal to (a) pi/2 (b) pi/4 (c) pi/12 (d) (3pi)/4

P_(1) and P_(2) are the lengths of the perpendicular from the foci on the tangent of the ellipse and P_(3) and P_(4) are perpendiculars from extermities of major axis and P from the centre of the ellipse on the same tangent, then (P_(1)P_(2)-P^(2))/(P_(3)P_(4)-P^(2)) equals (where e is the eccentricity of the ellipse)

The argument of (1-i)/(1+i) is a. -pi/2 b. pi/2 c. (3pi)/2 d. (5pi)/2

There exists a positive real number of x satisfying "cos"(tan^(-1)x)=xdot Then the value of cos^(-1)((x^2)/2)i s pi/(10) (b) pi/5 (c) (2pi)/5 (d) (4pi)/5

Let us consider an ellipse whose major and minor axis are 3x+4y-7=0 and 4x-3y-1=0 respectively. P be a variable point on the ellipse at any instance, it is given that distance of P from major and minor axis are 4 and 5 respectively. It is also given that maximum distance P from minor axis is 5sqrt(2) , then its eccentricity is 3/5 (b) 3/(sqrt(3)4) (c) 4/5 (d) None of these

The amplitude of sin (pi)/(5) +i(1-cos"" (pi)/(5)) is