The equation of the tangent to the curve (1 + x2) y
= 2 - X, where it crosses the x-axis, is
Choose the best option
X + 5y = 2
x - 5y = 2
5x - y = 2
5x + y - 2 = 0
Answers
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Step-by-step explanation:
ANSWER
Given curve can be written as, y=
1+x
2
2−x
To get the point where the above curve will cross the x-axis, put y=0
⇒0=
1+x
2
2−x
⇒x=2
Thus the required point is (2,0)
Now differentiate the given curve using quotient rule,
dx
dy
=
(1+x
2
)
2
(1+x
2
)(−1)−(2−x)(2x)
=
(1+x
2
)
2
x
2
−4x−1
Thus the slope of a tangent to this curve at point (2,0) is
m=
dx
dy
∣
∣
∣
∣
∣
(2,0)
=
(1+2
2
)
2
2
2
−4(2)−1
=−
25
5
=−
5
1
Therefore the slope of normal at this point will be 5
Hence required equation of normal is given by, (y−0)=5(x−2)
⇒5x−y−10=0
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