Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseGeneralMedium2 minQB

MathematicsMediuminteger

A circle concentric to an ellipse $\frac{4 x ^{2}}{289} + \frac{4 y ^{2}}{λ ^{2}} = 1 (λ < \frac{17}{2})$ passes through foci $F_{1}$ and $F_{2}$ cuts the ellipse at ' P ' such that area of triangle $P_{1} F_{2}$ is 30 sq.units. If $F_{1} F_{2} = 13 K$ where $K \in Z$ then $K =$

Answer:

Solution:

Since $F_{1} & F_{2}$ are the ends of the diameter Area of $Δ PF_{1} F_{2} = \frac{1}{2} (F_{1} P) (F_{2} P) = \frac{1}{2} x (17 - x) = 30 \Rightarrow x = 5$ or $12 \Rightarrow F_{1} F_{2} = 13$

Stream:JEESubject:MathematicsTopic:EllipseSubtopic:General

⏱ 2mℹ️ Source: QB

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