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MATH / A hyperbola centered at the origin has foci at (±7,0), and passes through the point (2,12). If the equation of the hyperbola is (x²)/(a²)−(y²)/(b²)=1,where a and b are positive con…

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problem

A hyperbola centered at the origin has foci at (±7,0),(\pm 7, 0), and passes through the point (2,12).(2, 12). If the equation of the hyperbola is x2a2−y2b2=1,\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1,where aa and bb are positive constants, compute the ordered pair (a,b).(a, b).
Plain-text mathematical notation (without MathML)
A hyperbola centered at the origin has foci at (±7,0), and passes through the point (2,12). If the equation of the hyperbola is (x²)/(a²)−(y²)/(b²)=1,where a and b are positive constants, compute the ordered pair (a,b).
Original LaTeX notation
A hyperbola centered at the origin has foci at $(\pm 7, 0),$ and passes through the point $(2, 12).$ If the equation of the hyperbola is \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1,\]where $a$ and $b$ are positive constants, compute the ordered pair $(a, b).$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
a08e7fba-f306-5ab5-a135-8889cdc1f54d
task_key
intermediate~5falgebra--test--a08e7fba-f306-5ab5-a135-8889cdc1f54d
task_revision_id
1
config / split
intermediate_algebra / test

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