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

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

Express the following in the standard form a+i b :1/(-2+sqrt(-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 .

Draw the graphs of the following parabolas : (i) x=y ^(2) - 2y -3 (ii) x = 6+y -y^(2)

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

Which one of the following curves cut the parabola at right angles? x^2+y^2=a^2 (b) y=e^(-x//2a) y=a x (d) x^2=4a y

Find the equation of each of the following parabolas. focus at (-1,-2) , directrix x-2y+3=0 .

Find the equation of line which is normal to the parabola x^(2)=4y and touches the parabola y^(2)=12x .

Consider a point P on a parabola such that 2 of the normal drawn from it to the parabola are at right angles on parabola, then If P -= (x _(1), y _(1)), the slope of third normal is, if If the equation of parabola is y^(2)= 8x

Name the conic by finding its standard-form equation. 4x^(2)+4y^(2)-12x-20y-2=0