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Byju's Answer
Standard XII
Mathematics
Axis
If the vertex...
Question
If the vertex of a parabola is
(
0
,
1
)
and its directrix is
2
y
=
5
, then its equation will be:
A
y
2
+
6
x
=
6
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B
y
2
+
6
y
=
6
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C
x
2
=
6
y
+
6
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D
x
2
+
6
y
=
1
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Solution
The correct option is
D
x
2
+
6
y
=
1
Equation of direction
⇒
y
=
5
2
Equation of tangent of vertex
⇒
y
=
1
⇒
(
y
−
1
)
=
0
distance between vertex & direction
=
3
⇒
0
x
+
2
y
−
5
=
0
(
0
,
1
)
0
+
2
−
5
2
=
−
3
2
equation of axis
⇒
x
=
0
eqn of parabola
⇒
x
2
=
4
(
−
3
2
)
(
y
−
1
)
x
2
=
−
6
(
y
−
1
)
x
2
+
6
y
=
6
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0
Similar questions
Q.
Circles
Number of common tangents
I:
x
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+
y
2
=
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x
2
+
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−
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a)
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II:
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=
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−
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−
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IV:
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−
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y
+
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=
0
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+
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+
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Q.
Let
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+
y
2
−
2
x
−
6
y
+
9
=
0
and
x
2
+
y
2
+
6
x
−
2
y
+
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=
0
be the equation of two circles. Then
Q.
The equation of the parabola whose focus lies at the intersection point of the lines
x
+
y
=
3
and
x
−
y
=
1
and directrix is
x
−
y
+
5
=
0
Q.
Find the equation of the circle which passes through the points of intersection of circles
x
2
+
y
2
−
2
x
−
6
y
+
6
=
0
and
x
2
+
y
2
+
2
x
−
6
y
+
6
=
0
and intersects the circle
x
2
+
y
2
+
4
x
+
6
y
+
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=
0
orthogonally.
Q.
The equation of the circle of radius 3 that lies in the second quadrant and touching the lines x = 0 and y = 0 is
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