If the tangent drawn at point `(t^2,2t)` on the parabola `y^2=4x` is the same as the normal drawn at point `(sqrt(5)costheta,2sintheta)` on the ellipse `4x^2+5y^2=20,` then `theta=cos^(-1)(-1/(sqrt(5)))` (b) `theta=cos^(-1)(1/(sqrt(5)))` `t=-2/(sqrt(5))` (d) `t=-1/(sqrt(5))`

y = sin^(-1)(x/sqrt(1+x^2)) + cos^(-1)(1/sqrt(1+x^2))

if the normal at the point t_(1) on the parabola y^(2) = 4ax meets the parabola again in the point t_(2) then prove that t_(2) = - ( t_(1) + 2/t_(1))

If sin2theta=cos3theta"and"theta is an acute angle, then sintheta equal (a) (sqrt(5)-1)/4 (b) -((sqrt(5)-1)/4) (c) (sqrt(5)+1)/4 (d) (-sqrt(5)-1)/4

Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))

Simiplify (1)/(7+4sqrt3)+(1)/(2+sqrt5)

Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=1 whose distance from the center of the ellipse is sqrt(5)

If tangents P Q and P R are drawn from a point on the circle x^2+y^2=25 to the ellipse (x^2)/16+(y^2)/(b^2)=1,(b (a) (sqrt(5))/4 (b) (sqrt(7))/4 (c) (sqrt(7))/2 (d) (sqrt(5))/3

No tangent can be drawn from the point (5/2,1) to the circumcircle of the triangle with vertices (1,sqrt(3)),(1,-sqrt(3)),(3,-sqrt(3)) .

The points on the line x=2 from which the tangents drawn to the circle x^2+y^2=16 are at right angles is (are) (a) (2,2sqrt(7)) (b) (2,2sqrt(5)) (c) (2,-2sqrt(7)) (d) (2,-2sqrt(5))

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))