By using properties of determinants. Show that: (i) `|(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2` (ii) `|(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)`

Using properties of determinants , find the value of k if |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|=k(x^(3)+y^(3)) .

Show that: (x^(2)+y^(2))^(5)=(x^(5)-10x^(3)y^(2)+5xy^(4))^(2)+(5x^(4)-10x^(2)y^(3)+y^(5))^(2)

{:(2x - 3y = k),(4x + 5y = 3):}

{:(2x - 4y = k),(5x - 10y = 7.5):}

The distance between the directrices of the ellipse (4x-8)^(2)+16y^(2)=(x+sqrt(3y)+10)^(2) is k,then (k)/(2) is

For which of the following, y can be a function of x, (x in R, y in R) ? {:((i) (x-h)^(2)+(y-k)^(2)=r^(2),(ii)y^(2)=4ax),((iii) x^(4)=y^(2),(iv) x^(6)=y^(3)),((v) 3y=(log x)^(2),""):}

{:(2x + 3y = 2),((k + 2)x + (2k + 1)y = 2(k - 1)):}