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The equation of the tangent to the parab...

The equation of the tangent to the parabola `y^(2) =9x`, which passes through the point `(4, 10)` is

A

`x+4y+1=0`

B

`9x+4y+4=0`

C

`x-4y+36=0`

D

`19x-14y+4=0`

Text Solution

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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=4x+(9)/(4m)`
`rArr 16m^(2)-40m+9=0`
`rArr m=(1)/(4) and m=(9)/(4)`
Tangents are `x-4y+36=0 and 9x-4y+4=0`
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