Find the center of the circle `x=-1+2costheta,y=3+2sintheta`

Find the length of normal to the curve x=a(theta+sintheta),y=a(1-costheta) at theta=pi/2dot

Find the length of normal to the curve x=a(theta+sintheta),y=a(1-costheta) at theta=pi/2dot

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4 . Then find the radius of the circle.

The equation of a circle is x^2+y^2=4. Find the center of the smallest circle touching the circle and the line x+y=5sqrt(2)

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is

Find the locus of the center of the circle touching the circle x^2+y^2-4y=4 internally and tangents on which from (1, 2) are making of 60^0 with each other.

Find the locus of the center of the circle touching the circle x^2+y^2-4y-2x=2sqrt3-1 Internally and tangents on which from (1, 2) are making of 60^0 with each other.

If costheta:sintheta=1:2 , then find the value of (8costheta-2sintheta)/(4costheta+2sintheta)

Find the equation of the curve whose parametric equation are x=1+4costheta,y=2+3sintheta,theta in Rdot

Find the center of the smallest circle which cuts circles x^2+y^2=1 and x^2+y^2+8x+8y-33=0 orthogonally.