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)`

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)|=y^2(3y+k)

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 )

By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2x2xx+4|=(5x-4)(4-x)^2 (ii) |y+k y y y y+k y y y y+k|=k^2(2ydotk)^2

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

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),""):}

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),""):}

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),""):}

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),""):}

Find the centre and radius of each of the following circle : (i) x^(2)+y^(2)+4x-4y+1=0 (ii) 2x^(2)+2y^(2)-6x+6y+1=0 (iii) 2x^(2)+2y^(2)=3k(x+k) (iv) 3x^(2)+3y^(2)-5x-6y+4=0 (v) x^(2)+y^(2)-2ax-2by+a^(2)=0