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

Convert rsintheta=rcostheta+4 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)

If roots of equation 3x^2+5x+1=0 are (sectheta_1-t a ntheta_1)a n d(cos e ctheta_2-cottheta_2)dot Then find the equation whose roots are (sectheta_1+t a ntheta_1)a n d(cos e ctheta_2+cottheta_2)dot

If cos e ctheta-sintheta=ma n dsectheta-costheta=n ,"eliminate"theta

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

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

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , pandqa r ei n t e g e r ss u c ht h a tn ,q"!="0andq m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

Find the parametric form of vector equation, and Cartesian equations of the plane containing the line vec(r)=(hat(i)-hat(j)+3hat(k))+t(2hat(i)-hat(j)+4hat(k))" and perpendicular to plane "vec(r)*(hat(i)+2hat(j)+hat(k))=8.