Question

Give the equation of a conic which is symmetric to the line x+2 = 0.

Answer 1

The equations of conic sections is simmetric to the line $x+2=0$ is

a) Circle $(x+2)^2+(y-k)^2=r^2$ center is $(-2,k),$ radius is $r$

b) Ellipse $\frac{(x+2)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ center is $(-2,k)$ length of major axis is $2a$ , length of minor axis is $2b$

c) Hyperbola $\frac{(x+2)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$ center is $(-2,k)$ distance between the vertices is $2a$

d) Parabola $(x+2)^2=4p(y-k)$ vertex is $(-2,k)$ , focus is $(-2,k+p)$ ,directrix is the line

$y=k-p$ , axis is the line $x=-2$