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Byju's Answer
Standard XII
Mathematics
Rolle's Theorem
find the coor...
Question
find the coordinates of the points on the curve y=x^2+3x+4, the tangents at which passes through the origin
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Solution
Let
the
required
point
is
x
1
,
y
1
Now
,
y
=
x
2
+
3
x
+
4
⇒
dy
dx
=
2
x
+
3
⇒
dy
dx
x
1
,
y
1
=
2
x
1
+
3
Now
,
equation
of
tangent
at
x
1
,
y
1
is
:
y
-
y
1
x
-
x
1
=
2
x
1
+
3
Since
the
tangent
passes
through
the
origin
0
,
0
,
so
-
y
1
-
x
1
=
2
x
1
+
3
⇒
y
1
=
2
x
1
2
+
3
x
1
.
.
.
1
But
x
1
,
y
1
lies
on
the
given
curve
,
so
y
1
=
x
1
2
+
3
x
1
+
4
.
.
.
.
2
Comapring
1
and
2
,
we
get
2
x
1
2
+
3
x
1
=
x
1
2
+
3
x
1
+
4
⇒
x
1
=
±
2
When
x
1
=
2
;
then
y
1
=
2
2
+
3
2
+
4
=
4
+
6
+
4
=
14
When
x
1
=
-
2
;
then
y
1
=
-
2
2
+
3
-
2
+
4
=
4
-
6
+
4
=
2
So
,
required
points
are
:
2
,
14
and
-
2
,
2
.
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Similar questions
Q.
The coordinates of the point on the curve
y
=
x
2
+
3
x
+
4
the tangent at which passes through the origin are -
Q.
Which of the following is (are) the coordinate(s) of the points on the curve
y
=
x
2
+
3
x
+
4
, the tangents at which pass through the origin?
