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Mathematics
Problem
Let
P
(
x
1
,
y
1
)
P(x_1, y_1)
P
(
x
1
,
y
1
)
and
Q
(
x
2
,
y
2
)
Q(x_2, y_2)
Q
(
x
2
,
y
2
)
,
y
1
<
0
,
y
2
<
0
y_1 < 0, y_2 < 0
y
1
<
0
,
y
2
<
0
be the end points of the latusrectum of the ellipse
x
2
+
4
y
2
=
4
x^2 + 4y^2 = 4
x
2
+
4
y
2
=
4
. The equations of parabolas with latusrectum
P
Q
PQ
P
Q
are a.
x
2
+
2
3
y
=
3
+
3
x^2 + 2\sqrt{3}y = 3 + \sqrt{3}
x
2
+
2
3
y
=
3
+
3
b.
x
2
−
2
3
y
=
3
+
3
x^2 - 2\sqrt{3}y = 3 + \sqrt{3}
x
2
−
2
3
y
=
3
+
3
c.
x
2
+
2
3
y
=
3
−
3
x^2 + 2\sqrt{3}y = 3 - \sqrt{3}
x
2
+
2
3
y
=
3
−
3
d.
x
2
−
2
3
y
=
3
−
3
x^2 - 2\sqrt{3}y = 3 - \sqrt{3}
x
2
−
2
3
y
=
3
−
3
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