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MATH / Let F₁ and F₂ be the foci of the ellipse kx²+y²=1, where k>1 is a constant. Suppose that there is a circle which passes through F₁ and F₂ and which lies tangent to the ellipse at t…

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problem

Let F1F_1 and F2F_2 be the foci of the ellipse kx2+y2=1,kx^2 + y^2 = 1, where k>1k > 1 is a constant. Suppose that there is a circle which passes through F1F_1 and F2F_2 and which lies tangent to the ellipse at two points on the xx-axis. Compute k.k.
Plain-text mathematical notation (without MathML)
Let F₁ and F₂ be the foci of the ellipse kx²+y²=1, where k>1 is a constant. Suppose that there is a circle which passes through F₁ and F₂ and which lies tangent to the ellipse at two points on the x-axis. Compute k.
Original LaTeX notation
Let $F_1$ and $F_2$ be the foci of the ellipse $kx^2 + y^2 = 1,$ where $k > 1$ is a constant. Suppose that there is a circle which passes through $F_1$ and $F_2$ and which lies tangent to the ellipse at two points on the $x$-axis. Compute $k.$

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
c97099eb-3d86-5882-a38d-e7ba36b1442d
task_key
intermediate~5falgebra--test--c97099eb-3d86-5882-a38d-e7ba36b1442d
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import