" 2.(i) "x=at^(2),y=2at

If x=(sqrt(5)-2)/(sqrt(5)+2) and y=(sqrt(5)+2)/(sqrt(5)-2): find (i) x^(2)" (ii) "y^(2) (iii) xy " (iv) "x^(2)+y^(2)+xy

Show that each of the following expressions is a soluton of the corresponding given differential equation (i) y=2x^(2),xy'=2y (ii) y=ae^(x)+be^(-x), y''-y=0

Find the latus rectum,the eccentricity,and the coordinates of the foci,of the ellipses.( i ) x^(2)+3y^(2)=a^(2)

The complex numbrs x and y such that x,x+2y,2x+y are n A.P. and (y+1)^2, xy+5, (x+1)^2 are in G.P. are (A) x=3, y=1 (B) x=-1+2sqrt(2)i, y=1/3 (-1+2sqrt(2)i) (C) x=sqrt(2)+i, y=3sqrt(5)-sqrt(2)i (D) x=-1(1+2sqrt(2)i), y= - 1/3 (1+2sqrt(2)i)

The complex numbrs x and y such that x,x+2y,2x+y are n A.P. and (y+1)^2, xy+5, (x+1)^2 are in G.P. are (A) x=3, y=1 (B) x=-1+2sqrt(2)i, y=1/3 (-1+2sqrt(2)i) (C) x=sqrt(2)+i, y=3sqrt(5)-sqrt(2)i (D) x=-1(1+2sqrt(2)i), y= - 1/3 (1+2sqrt(2)i)

Find the parametric equation of the circles : (i) 2x^(2) + 2y^(2) - 5x - 7y - 3 = 0 (ii) 3x^(2) + 3y^(2) + 4x - 6y - 4 = 0 .

Form the differential equation of the family of curves represented by the equation (a being the parameter): (i) (2x+a)^2+y^2=a^2 (ii) (2x-a)^2-y^2=a^2 (iii) (x-a)^2+2y^2=a^2

Find the point at which is shifted such that the transformed equations of the following equations has no first degree term : (i) 2x^(2)+3y^(2)+4x-12y+10=0 (ii) x^(2)+y^(2)-xy-5x+4y+5=0

If origin is shifted to point (1,-2) then find the new transformed form of the following equation. (i) 2x^(2) + y^(2) - 4x+ 4y =0 (ii) y^(2) - 4x + 4y + 8=0