Question

focus=(2,3), directrix :x-2y-6=0, e=1.find the conic section.

Answer 1

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Answer 2

As, e=1

Thus, the conic is a parabola.

$\sqrt{(x - 2) {}^{2} + {(y - 3)}^{2} } = | \frac{x - 2y - 6}{ \sqrt{5} } |$

$5(x - 2 {)}^{2} +5 {(y - 3)}^{2} = {(x - 2y - 6)}^{2}$

$5 {x}^{2} -20x + 20 + 5 {y}^{2} - 30y + 45 = {x }^{2} + 4 {y}^{2} + 36 - 4xy + 24y - 12x$

$4 {x}^{2} + {y}^{2} + 4xy - 8x - 54y + 29 = 0$