Given:
Identify the focus and directrix of the following parabola
(a) y^2 = 3x^2
Solution:
1) It is not a parabola
Possible solutions:
2) If there is a mistake in the left part of the equation and it should be like:
y=3x2
Then, remembering the normal form of parabola:
(x−h)2=4p(y−k)
Reshaping our equation:
(x−0)2=4∗1/4∗1/3∗(y−0)
(x−0)2=4∗1/12(y−0)
From which:
h=0;p=1/12;k=0
Focus and directrix are:
focus=(h,k+p);directrix:y=k−p
In our case:
focus=(0,1/12);directrix:y=−1/12
3) If there is a mistake in the right part of the equation and it should be like:
y2=3x
The normal form of parabola in that case:
(y−k)2=4p(x−h)
In our case:
(y−0)2=4∗1/4∗3x2
(y−0)2=4∗3/4∗x2
From which:
k=0;p=3/4;h=0
Focus and directrix are:
focus=(h+p,k);directrix:x=h−p
In our case:
focus=(3/4,0);directrix:x=−3/4
Answer:
It is not a parabola
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