query: What is the shortest distance from the ellipse $x^2+\frac{y^2}{4} =1$ and the point (2,2).
positive_passages.docid: 156561
positive_passages.text: Minimizing distance between an ellipse and a point
negative_passages.docid: 9658
negative_passages.text: What is the length of a sine wave from $0$ to $2\pi$?
negative_passages.docid: 61641
negative_passages.text: Equations of lines tangent to an ellipse
negative_passages.docid: 17545
negative_passages.text: Tangent lines to ellipse from external point
negative_passages.docid: 101570
negative_passages.text: If derivative of function is less than or equal to 4, prove the existence of point $c$ so $f(c)=c^2$.
negative_passages.docid: 118723
negative_passages.text: Finding the tangents common to two rotated ellipses?
negative_passages.docid: 57736
negative_passages.text: Minimum value of $\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$
negative_passages.docid: 151502
negative_passages.text: Finding the inverse of the arc length function
negative_passages.docid: 77983
negative_passages.text: Shortest method for $\int_{0}^{1}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}$
negative_passages.docid: 6707
negative_passages.text: Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
negative_passages.docid: 37448
negative_passages.text: Two Circles and Tangents from Their Centers Problem
negative_passages.docid: 114861
negative_passages.text: equation $\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x^2}+\frac{1}{y^2}}$
negative_passages.docid: 120379
negative_passages.text: The Path of the center of a cutting tool that will cut out an ellipse (x/4)2+(y/2)2=1
negative_passages.docid: 56195
negative_passages.text: Find the minimum value of $\sin^{2} \theta +\cos^{2} \theta+\sec^{2} \theta+\csc^{2} \theta+\tan^{2} \theta+\cot^{2} \theta$
negative_passages.docid: 109997
negative_passages.text: Derivation of the polar form of an ellipse from first principles
negative_passages.docid: 24730
negative_passages.text: A circle has the same center as an ellipse and passes through the foci $F_1$ and $F_2$ of the ellipse, two curves intersect in $4$ points.
negative_passages.docid: 149983
negative_passages.text: What is average distance from center of square to some point?