find the equation of parabola with focal width 16 axis parallel to x axis and passing through the points (3,7) and (3,-1)
Answers
Answer:
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Step-by-step explanation:
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Given : parabola with focal width 16 axis parallel to x axis and passing through the points (3,7) and (3,-1)
To Find :
Solution:
parabola parallel to x axis
( y - k)² = 4p(x - h)
4p = focal width = 16
=> ( y - k)² = 16(x - h)
passing through the points (3,7) and (3,-1)
=> (7 - k)² = 16(3 - h)
(-1 - k)² = 16(3 - h)
(7 - k)² = (-1 - k)²
=> 49 + k² - 14k = k² + 2k + 1
=> 16k = 48
=> k = 3
(7 - k)² = 16(3 - h)
=> (7 -3)² = 16(3 - h)
=> 4² = 16(3 - h)
=> 3 - h = 1
=> h = 2
( y - 3)² = 16(x - 2)
equation of parabola is ( y - 3)² = 16(x - 2)
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