Vertex is (4, 3) and diretctrix is 3x + 2y – 7 = 0 then equation of latusrectum is

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3x+2y–18=0

3x+2y–29 = 0

3x+2y–8 = 0

3x+2y–31= 0

answer is B.

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Detailed Solution

Given that vertex is $(4, 3)$ and the directrix is $3 x + 2 y - 7 = 0$

The latus rectum is a line parallel to the directrix, and it is in the form of $3 x + 2 y + k = 0$

The midway between the directrix and latursrectum is passing through the vertex

hence, $3 x + 2 y + (\frac{k - 7}{2}) = 0$ passes through the point $(4, 3)$

Hence,

$\begin{array}{rcl} 12 + 6 + \frac{k - 7}{2} & = & 0 \\ \frac{k - 7}{2} & = & - 18 \\ k & = & - 29 \end{array}$

Therefore, the equation of the latusrectum is $3 x + 2 y - 29 = 0$

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