║⊕QUESTION⊕║
Everything around you is mathematics. Everything around you is numbers.
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CLASS 11
THE HYPERBOLA
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Find the equation to the hyperbola whose eccentricity is 2, whose focus is (2,0) and whose directrix is x - y = 0
Answers
SOLUTION
Let we understand what the basics behind the figure like hyperbola and all the figure in conic section.
If a pencil moves on a paper such that the Ratio of distance of the point from a Fix point (Focus) with the fix line (directrix) is constant greater than 1(known as eccentricity) than the figure drawn on paper is Hyperbola.
let (X,y) be the point of any moving particle on hyperbola than ACC to definition.....
Distance of point from focus = Distance from directrix
√(X -2)² + (y-0)² = 2(X - y)/√2
square on both side.
(x - 2)² + y² = 4(x - y)²/2
(x - 2)² + y² = 2(x - y)²
(x² + 4 - 4x) + y² = 2x² + 2y² - 4xy
x² + 4 - 4x + y² = 2x² + 2y² - 4xy
x² + y² + 4x - 4xy - 4 = 0
Distance of a point (X,y) from a line ax + by + c can be written as....
| (aX + by + c) |/√a²+b²
Sorry for any mistake....
Answer:
I hope it's help you
SORRY IF IN MY ANSWER ANY MISTAKE
