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))`

Find the equation of the normal to the circle x^2+y^2=9 at the point (1/(sqrt(2)),1/(sqrt(2))) .

Find the length of the tangent from the point (7,2) to the circle 2x^(2)+2y^(2)+5x+y=15

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (a) (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

If two chords drawn from the point A(4,4) to the parabola x^2=4y are bisected by the line y=m x , the interval in which m lies is (a) (-2sqrt(2),2sqrt(2)) (b) (-oo,-sqrt(2))uu(sqrt(2),oo) (c) (-oo,-2sqrt(2)-2)uu(2sqrt(2)-2,oo) (d) none of these

The normal at a point P on the ellipse x^2+4y^2=16 meets the x-axis at Qdot If M is the midpoint of the line segment P Q , then the locus of M intersects the latus rectums of the given ellipse at points. (a) (+-((3sqrt(5)))/2+-2/7) (b) (+-((3sqrt(5)))/2+-(sqrt(19))/7) (c) (+-2sqrt(3),+-1/7) (d) (+-2sqrt(3)+-(4sqrt(3))/7)

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 (a) theta=cos^(-1)(-1/(sqrt(5))) (b) theta=cos^(-1)(1/(sqrt(5))) (c) t=-2/(sqrt(5)) (d) t=-1/(sqrt(5))

A beam of light is sent along the line x-y=1 , which after refracting from the x-axis enters the opposite side by turning through 30^0 towards the normal at the point of incidence on the x-axis. Then the equation of the refracted ray is (a) (2-sqrt(3))x-y=2+sqrt(3) (b) (2+sqrt(3))x-y=2+sqrt(3) (c) (2-sqrt(3))x+y=(2+sqrt(3)) (d) y=(2-sqrt(3))(x-1)

The values of parameter a for which the point of minimum of the function f(x)=1+a^2x-x^3 satisfies the inequality (x^2+x+2)/(x^2+5x+6)<0a r e (a) (2sqrt(3),3sqrt(3)) (b) -3sqrt(3),-2sqrt(3)) (c) (-2sqrt(3),3sqrt(3)) (d) (-2sqrt(2),2sqrt(3))

In a A B C , if tanA:tanB :tanC=3:4:5, then the value of sinA sinB sinC is equal to (a) 2/(sqrt(5)) (b) (2sqrt(5))/7 (2sqrt(5))/9 (d) 2/(3sqrt(5))

If C_1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair of tangents on C_1, where P is any point on the director circle of C_1, then the radius of the smallest circle which touches c_1 externally and also the two tangents P A and P B is (a) 2sqrt(3)-3 (b) 2sqrt(2)-1 (c) 2sqrt(2)-1 (d) 1