Hello
I am a bit stuck with calculating my hyperbola from some properties. Namely Focus (±ae,0) of (4,0) and directrix (±a/e) x = 3.
This is my current calculation, but the problem is my b^2 is negative which doesn't seem right.
1) ae = 4
2) a/e = 3
Multiply 1 & 2: a^2 = 12, so a = 6
solve e using a for equation 1:
6e = 4 so e = 4/6
Now to solve b^2 for my equation i get:
b^2 = 6^2((4/6)^2 - 1) = -20
Which would give an equation for my hyperbola as:
x^2/12 + y^2/20 = 1
But this is an ellipse so where have i gone wrong?
I am a bit stuck with calculating my hyperbola from some properties. Namely Focus (±ae,0) of (4,0) and directrix (±a/e) x = 3.
This is my current calculation, but the problem is my b^2 is negative which doesn't seem right.
1) ae = 4
2) a/e = 3
Multiply 1 & 2: a^2 = 12, so a = 6
solve e using a for equation 1:
6e = 4 so e = 4/6
Now to solve b^2 for my equation i get:
b^2 = 6^2((4/6)^2 - 1) = -20
Which would give an equation for my hyperbola as:
x^2/12 + y^2/20 = 1
But this is an ellipse so where have i gone wrong?