Question

find the equation of tangent and normals to curve at the point on it
(iv) 2xy + r sin y = 2tt at
​

Answer 1

Answer:

x

2

+2xy−3y

2

=0

This is the equation of a pair of straight lines.

(x−y)(x+3y)=0

2x+2y+2xy

′

−6yy

′

=0

⇒

3y−x

x+y

=y

′

At (1,1)

the slope of the tangent is y

′

=1.

The slope of the normal is −1.

Hence,

The normal has the equation : x+y=2

We need to find its intersection with x+3y=0

On solving we get,

2−y+3y=0⇒2y=−2

y=−1,x=3

Hence, it meets it in the fourth quadrant.