KEAM 2011 Math Paper

Curve, y=‌

1

x2+2x+5

....(i)
Let the equation of line which is parallel to x -axis is,
y=c....(ii)
The line (ii) is a tangent to curve (i), then slope of curve = slope of line
‌

−(2x+2)

(x2+2x+5)2

=0
(∵‌

dy

dx

=‌

−(2x+2)

(x2+2x+5)2

)
⇒‌‌x=−1
From Eq. (i),
y=‌

1

1−2+5

=‌

1

4

From Eq. (ii),
c=‌

1

4

Hence, the required equation of line is, y=‌

1

4

.