Find the length of the latus rectum of the parabola whose focus is at (2, 3) and directrix is the line `x-4y+3=0` .

Explanation

We have given focus `= (2,3) `& equation of directrix `=x−4y+3=0`

Now we have to find Length of latus rectum

Now, let `P(x,y)` be the Point on the parabola

So, `PN` be a perpendicular from `P` on the directrix.

then, we have `(SP)^2=(PN)^2`

`(x−2)^2+(y−3)^2=((x−4y+3)/sqrt(1^2+(−4)^2))^2`

`x^2−4x+4+y^2−6y+9= ((x+4y+3)^2)/17`

`17x^2+17y^2−68x−102y+221=x^2+16y^2+9−8xy+6x−24y`

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