benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Let F₁=(10,2) and F₂=(−16,2). Then the set of points P such that

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let F1=(10,2)F_1 = (10,2) and F2=(−16,2).F_ 2= (-16,2). Then the set of points PP such that |PF1−PF2|=24|PF_1 - PF_2| = 24form a hyperbola. The equation of this hyperbola can be written as (x−h)2a2−(y−k)2b2=1.\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.Find h+k+a+b.h + k + a + b.
Plain-text mathematical notation (without MathML)
Let F₁=(10,2) and F₂=(−16,2).  Then the set of points P such that
|PF₁−PF₂|=24form a hyperbola.  The equation of this hyperbola can be written as
((x−h)²)/(a²)−((y−k)²)/(b²)=1.Find h+k+a+b.
Original LaTeX notation
Let $F_1 = (10,2)$ and $F_ 2= (-16,2).$  Then the set of points $P$ such that
\[|PF_1 - PF_2| = 24\]form a hyperbola.  The equation of this hyperbola can be written as
\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.\]Find $h + k + a + b.$

level

Level 4

type

Intermediate Algebra

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
60f1c881-ffd8-5a60-abff-5c519cf7ba16
task_key
intermediate~5falgebra--test--60f1c881-ffd8-5a60-abff-5c519cf7ba16
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import