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Mathematics
The normal to the curve y(x-2)(x-3)=x+6 at the point where the curve intersects the y-axis passes through the point :
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Q. The normal to the curve
y
(
x
−
2
)
(
x
−
3
)
=
x
+
6
at the point where the curve intersects the y-axis passes through the point :
JEE Main
JEE Main 2017
Application of Derivatives
A
(
1
2
,
1
2
)
38%
B
(
1
2
,
−
1
3
)
50%
C
(
1
2
,
1
3
)
0%
D
(
−
1
2
,
−
1
2
)
12%
Solution:
y
(
x
−
2
)
(
x
−
3
)
=
x
+
6
At y-axis,
x
=
0
,
y
=
1
Now, on differentiation.
d
y
d
x
(
x
−
2
)
(
x
−
3
)
+
y
(
2
x
−
5
)
=
1
d
y
d
x
(
6
)
+
1
(
−
5
)
=
1
d
y
d
x
=
6
6
=
1
Now slope of normal
=
−
1
Equation of normal
y
−
1
=
−
(
x
−
0
)
y
+
x
−
1
=
0
... (i)
Line(i) passes through
(
1
2
,
1
2
)