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Question

Latus rectum of the parabola whose focus is (3,4) and whose tangent at vertex has the equation x + y = 7 + 5√2 is ?


Solution

length og latus rectum of a parabola is equal to 4 times the distance between the focus and the vertex of the parabola,
so here focus is (3,4)
and the distance between the focus of the parabola and ver tex is the perpendicular distance between the tangent through the vertex and the focus as the tangent thruogh the vertex will always be perpendicular to the axis
so this distance is the distnce between (3,4)
and the line x+y-7-5*2^(.5)
ie,|3+4-7-5*2^(.5)|/2^(.5)|=5
so the length of latus rectum is 4*5=20

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