Question

The ratio of length of latus rectum of parabola $y^2=16x$ and translated parabola $y^2+17=8x+2y$ is

Answer 1

First, we know that length of latus rectum does not change on translating the parabola.
So, length of latus rectum will be $4a.$
Now, for parabola $y^2=16x$ length of latus rectum will be $16.$
Also, rearranging the parabola
$y^2+17=8x+2y$
we get,
$\Rightarrow y^2-2y+1=8x-16$
$\Rightarrow (y-1{)}^2=8(x-2)$
So, length of latus rectum of this translated parabola is $8.$
Hence, the ratio of lengths of latus rectum of standard parabola and translated parabola is $\frac{16}{8}=2.$