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Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseTangent to ellipseMedium2 minQB

MathematicsMediumsingle choice

The lines $3 x + 5 y = 20$ and $3 x - 5 y = 20$ are tangents at the ends of a latus rectum of an origin-centred ellipse. Find the latus-rectum length.

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Answer:

Solution:

Their intersection lies on the directrix, giving $a / e = 20/3$ , while the tangent slope gives $e = 3/5$ . Thus $a = 4, b^{2} =$ $256/25$ , and $2 b^{2} / a = 5.12$ .

Stream:JEESubject:MathematicsTopic:EllipseSubtopic:Tangent to ellipse

⏱ 2mℹ️ Source: QB

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