Question

Match the conics with their respective length of latus rectum

Answer 1

1) $x^2/9+y^2/16=1$ is an ellipse with major axis along y-axis of length 4 and minor axis along x-axis of length 3 so the length of the latus rectum$=2\times \frac{3^2}{4}=4.5$
2) $x^2/16-y^2/25=1$ is an hyperbola with transverse axis along x-axis of length 4 and conjugate axis along y-axis of length 5.
So length of the latus rectum$=2\times \frac{25}{4}=12.5$
3) $x^2-y^2=4$ is a rectangular hyperbola with lengths of transverse and conjugate axis equal to 2 each.
So the length of the latus rectum$=2\times \frac{2^2}{2}=4$
4) $y^2=4(x-4)$ is a parabola whose equation can be written as $Y^2=4X$ where $Y=y,X=x-4$
So the length of the latus rectum $=4$