Vector Equation of a conic

Geometry Level 4

The equation ∣ r − i ∣ + ∣ r − j ∣ = 1 | r- i | +| r -j |=1 , where i i and j j are unit vectors perpendicular to each other, represents __________ \text{\_\_\_\_\_\_\_\_\_\_} .

This problem is a part of the set Advanced is basic .
A hyperbola An Ellipse A line segment No locus A circle

Keshav Tiwari by Keshav Tiwari , 23, India

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1 solution

Mark Hennings
Aug 14, 2016

For any point in the plane, the Triangle inequality gives ∣ r − i ∣ + ∣ r − j ∣ ≥ ∣ i − j ∣ = 2 |\mathbf{r} - \mathbf{i}| + |\mathbf{r}-\mathbf{j}| \ge |\mathbf{i}-\mathbf{j}| = \sqrt{2} So no points on the plane satisfy the given equation.

10 Helpful 2 Interesting 0 Brilliant 1 Confused

Couldn't we use something new

Biswajit Barik - 3 years, 11 months ago

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