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The equation of the tangent to the parab...

The equation of the tangent to the parabola `y^2 = 9x` which goes through the point `(4, 10)` is (A) `x+4y+1=0` (B) `9x+4y+4=0` (C) `x-4y+36=0` (D) `9x-4y+4=0`

A

`x+4y+1=0`

B

`9x+4y+4=0`

C

`x-4y+36=0`

D

`19x-14y+4=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Equation of tangent to the parabola
`y^(2)=9x`
`y= mx +(9)/(4m)" "…(i)`
Point (4,10) lies on this tangent `10=4m+(9)/(4m)`
`rArr 16m^(2) -40m +9=0 rArr m=(1)/(4)& m=(9)/(4) " " :.` Tangents are
`x-4y+36=0 & 9x-4y+4=0`
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