Convert `rsintheta=rcostheta+4` into its equivalent Cartesian equation.

Convert r=cos e cthetae^(rcostheta) into its equivalent Cartesian equation.

Convert r=4tanthetasectheta into its equivalent Cartesian equation.

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) (2,pi) (ii) (sqrt(3),pi//6)

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) (2,pi/6) (ii) (2,(11pi)/6)

Given the plane 5x-2y+4z-9=0 i.Find the coordinates of foot of the perpendicular from the origin to the plane. ii. Find the vector equation and the cartesian equation of this perpendicular .

Find the non-parametric form of vector equation, and Cartesian equation vector equation, and Cartesian equation of the plane passing through the point (0, 1,-5) and parallel to the straight lines vecr=(hati=2hatj-4hatk)+s(2hati+3hatj+6hatk) and vecr=(hati=3hatj-4hatk)+t(hati+hatj+hatk)

Find the parametric form of vector equation and Cartesian equations of a straight line passing through (5,2,8) and is perpendicular to the straight lines

Find the vector equation of line passing through A(3,4-7)a n dB(1,-1,6)dot Also find its Cartesian equations.