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))`

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

If y = 2sqrt2x+c is a tangent to the circle x^(2) +y^(2) = 16 , find the value of c.

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

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

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

The abscissa of the point on the curve sqrt(x y)=a+x the tangent at which cuts off equal intercepts from the coordinate axes is -a/(sqrt(2)) (b) a//sqrt(2) (c) -asqrt(2) (d) asqrt(2)

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)

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)