Question

What is the equation in standard form of the parabola with a focus at (2,3) and a directrix of y= 9?

Answer 1

`x^2-4x+12y-68=0`

Explanation:

`"for any point "(x,y)" on the parabola"`

`"the distance from "(x.y)" to the focus and directrix"`
`"are equal"`

`"using the "color(blue)"distance formula"`

`"with "(x,y)to(2,3)`

`rArrsqrt((x-2)^2+(y-3)^2)=|y-9|`

`color(blue)"squaring both sides"`

`(x-2)^2+(y-3)^2=(y-9)^2`

`rArrx^2-4x+4+y^2-6y+9=y^2-18y+81`

`rArrx^2-4x+12y-68=0`