Math, asked by kumarisunita1986, 5 months ago

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

Answered by mamtachoudhary9611
0

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

please mark it as brainliest

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