If the line `xcostheta=2` is the equation of a transverse common tangent to the circles `x^2+y^2=4` and `x^2+y^2-6sqrt(3)x-6y+20=0` , then the value of `theta` is `(5pi)/6` (b) `(2pi)/3` (c) `pi/3` (d) `pi/6`

If the line x cos theta+y sin theta=2 is the equation of a transverse common tangent to the circles x^(2)+y^(2)=4 and x^(2)+y^(2)=6sqrt(3)x-6y+20=0, then the value of theta is (5 pi)/(6) (b) (2 pi)/(3)( c) (pi)/(3)(d)(pi)/(6)

If the equation of tangent to the circle x^(2)+y^(2)-2x+6y-6=0 and parallel to 3x-4y+7=0 is 3x-4y+k=0 then the values of k are

cot^(-1)(-sqrt3)= (a) -pi/6 (b) (5pi)/6 (c) pi/3 (d) (2pi)/3

The line tangent to the curves y^(3)-x^(2)y+5y-2x=0 and x^(2)-x^(3)y^(2)+5x+2y=0 at the origin intersect at an angle theta equal to (pi)/(6) (b) (pi)/(4) (c) (pi)/(3) (d) (pi)/(2)

The angles at which the circles (x-1)^(2)+y^(2)=10andx^(2)+(y-2)^(2)=5 intersect is (pi)/(6) (b) (pi)/(4) (c) (pi)/(3) (d) (pi)/(2)

If t a ntheta+s e ctheta=sqrt(3),\ 0

From the point P(2+3sqrt(2)cos theta,3+3sqrt(2)sin theta),0

For f(x)=sin^2x ,x in (0,pi) point of inflection is: pi/6 (b) (2pi)/4 (c) (3pi)/4 (d) (4pi)/3

If the tangent at the point P(theta) to the ellipse 16x^(2)+11y^(2)=256 is also a tangent to the circle x^(2)+y^(2)-2x=15, then theta=(2 pi)/(3)( b )(4 pi)/(3) (c) (5 pi)/(3) (d) (pi)/(3)

The angle subtended by common tangents of two ellipses 4(x-4)^2+25 y^2=100a n d4(x+1)^2+y^2 at the origin is pi/3 (b) pi/4 (c) pi/6 (d) pi/2