Question

find the equation of tangent at (1,2) on the curve x²+y²=5​

Answer 1

Let (x,y) be the required point.

The slop of line 2x+3y=7 is

3

−2

.

⇒ x

2

+y

2

=13 ---- ( 1 )

⇒ 2x+2y

dx

dy

=0

⇒

dx

dy

=

y

−x

Slop of the tangent at (x,y)=

dx

dy

=

y

−x

Slope of the tangent = Slop of the given line

⇒

y

−x

=

3

−2

⇒ x=

3

2y

---- ( 2 )

From equation ( 1 ), we get

⇒ (

3

2y

)

2

+y

2

=13

⇒

9

13y

2

=13

⇒ y

2

=9

⇒ y=±3

⇒ y=3 or y=−3

And from equation ( 2 ),

⇒ x=

3

2(3)

=2 or x=

3

2(−3)

=−2

∴ The required points are (2,3) and (−2,−3).