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Secant of a Curve y =f(x)

The focus and...

Question

The focus and directrix of a parabola are (1,2) and 2x-3y+1=0. Then the equation of the tangent at vertex is

A

4x-6y+5=0

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B

4x-6y+9=0

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C

4x-6y+11=0

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D

4x-6y+7=0

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Solution

The correct option is A
4x-6y+5=0

$S = (2, 1) D i r e c t r i x 2 x - 3 y + 1 = 0$ Eqn of L.R is
$2 (x - 1) - 3 (y - 2) = 0$
$∴$ Eqn of tgt at vertex is $\Rightarrow 2 x - 3 y + 4 = 0$
$2 x - 3 y + \frac{1 + 4}{2} = 0 \Rightarrow 4 x - 6 y + 5 = 0$

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