[16.(1)/(2x)+(1)/(3y)=2],[(1)/(3x)+(1)/(2y)=(13)/(6)]

(1)/(2)+(1)/(4)+(1)/(8)+(1)/(16)+....=x,(1)/(3)+(1)/(9)+(1)/(21)+(1)/(81)+...=y then 2x+4y=

Find the centre and radius of each of the following circles : (i) (x - 3)^(2) + (y- 1) ^(2) = 9 (ii) (x - (1)/(2) ) ^(2) + ( y + (1)/(3) ) ^(2) = (1)/(16) (iii) (x + 5) ^(2) + ( y- 3 ) ^(2) = 20 (iv) x ^(2) + (y- 1 ) ^(2) = 2

(x^(2))/(36)+(y^(2))/(16)=1

The equation of the ellipse having a vertex at (6,1) a focus at (4,1) and the eccentricity (3)/(5) is 1) ((x-1)^(2))/(16)+((y-1)^(2))/(25)=1 (2) ((x-1)^(2))/(25)+((y-1)^(2))/(16)=1 3) ((x+1)^(2))/(25)+((y+1)^(2))/(16)=1 (4) ((x+1)^(2))/(16)+((y+1)^(2))/(25)=1

16. "4^(x)-3^(x-(1)/(2))=3^(x+(1)/(2))-2^(2x-1).

An ellipse has its centre at (1,-1) and semi major axis =8 and it passes through the point (1,3). The equation of the ellipse is ((x+1)^(2))/(64)+((y+1)^(2))/(16)=1b((x-1)^(2))/(64)+((y-1)^(2))/(16)=1c((x-1)^(2))/(64)+((y-1)^(2))/(16)=1d((x-1)^(2))/(64)+((y-1)^(2))/(16)=1

Solve : 8 ^(x+1) = 16 ^(y+2) and ( (1)/(2)) ^(3+x) = ((1)/(4))^(3y)

The ecfentricity of the ellipse ((x-1)^(2))/(2) + (y + (3)/(4)) ^(2)= (1)/(16) is