Question

find the slope of tangent on the curve x²+y²-4x-1=0at (3,2)​

Answer 1

Answer:

here is your answer

Explanation:

x

2

+y

2

−2x−4y+1

⇒2x+2y

dx

dy

−2−4

dx

dy

=0

⇒x+y

dx

dy

−1−2

dx

dy

=0 ⇒ (y−2)

dx

dy

=(1−x)

dx

dy

=

(1−x)

(y−2)

for the tangents to be parallel to y− axis,

dx

dy

=0

∴

dx

dy

=

(1−x)

(y−2)

=0 ⇒y=2

When y=2

x

2

+2

2

−2x−4(2)+1=0 ⇒x

2

+4−2x−8+1=0

⇒x

2

−2x−3=0 ⇒(x−1)(x−3)=0 ⇒x=−1 or 3

So, the points where tangents are parallel to y− axis

=(−1,2),(3,2)

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