Transform the following parabolas to the standard forms:
`(x+3)^(2)=8(y-5)`

Transform the following parabolas to the standard forms: (y-2)^(2)=2(x+1)

Write the following rational numbers in standard form: (-3)/(-8)

Write the following numbers in standard form. (2)/(-3)

Reduce the following equation of parabola to a standard form, hence find the vertex focus and the equations of the directrix and equation of latus rectum : 4x-y^(2)+2y-13=0 .

Transform the equation x^(2)+y^(2)=ax into polar form.

Express each of the following in factors form, ( 5x- 3y ) ^(3)+ (3y - 8z)^(3) + (8z - 5x) ^(3)

Write the following sets in tabular form : (i) {:x : x = (2n)/(n+2), n in W and n lt 3 } (ii) {x : x = 5y-3, y in Z and -2 le y lt 2 } (iii) {x : x in W " and " 8x + 5 lt 23}

Find the length of the latus rectum of the parabola x^(2) = -8y .

Find the vertex , focus, axis, directrix and latus rectum of the following parabola: y^2=8x+8y

A parabola is drawn touching the axis of x at the origin and having its vertex at a given distance k form this axis Prove that the axis of the parabola is a tangent to the parabola x^2=-8k (y-2k) .