Question

The equation of the tangent to the parabola y2 = 9x which goes through the point(4,10)

Answer 1

Answer:

x−4y+36=0

Equation of a tangent to a parabola is given by,

y=mx+

m

a

------ ( 1 )

In the given parabola, y

2

=9x

⇒ 4a=9

⇒ a=

4

9

Putting value of a in ( 1 ) we get,

y=mx+

4x

9

----- ( 2 )

As the given tangent passing through point (4,10)

∴ 10=4m+

4m

9

----- ( 2 )

⇒ 16m

2

−40m+9=0

⇒ 16m

2

−36m−4m+9=0

⇒ 4m(4m−9)−1(4m−9)=0

⇒ (4m−9)(4m−

4

1

)=0

⇒ m=

4

9

and m=

4

1

When m=

4

9

,

⇒ y=

4

9

x+1

⇒ 4y=9x+4

⇒ 9x−4y+4=0

When m=

4

1

,

⇒ y=

4

1

x+9

⇒ 4y=x+36

⇒ x−4y+36=0

∴ The required equations are 9x−4y+4=0 and x−4y+36=0

Step-by-step explanation:

answer: x-4y+36=0

Hope it helps

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