Question

Find the eq" of the tangent n to curve 47² +9y² = 40 al (42)​

Answer 1

Step-by-step explanation:

Given, equation of parabola is y

2

=4ax

Differentiating w.r.t. x, we get

2y

dx

dy

=4a

⇒

dx

dy

=

y

2a

Slope of the tangent at (at

2

,2at) is

(

dx

dy

)

(at

2

,2at)

=

2at

2a

=

t

1

Equation of the tangent at (at

2

,2at) is given by,

y−2at=

t

1

(x−at

2

)

⇒ty−2at

2

=x−at

2

⇒ty=x+at

2

Slope of normal at (at

2

,2at) is given by,

Slope of the tangent at(at

2

,2at)

−1

=−t

Equation of the normal at (at

2

,2at) is given by

y−2at=−t(x−at

2

)

⇒y−2at=−tx+at

3

⇒y=−tx+2at+at

3