A parabola with a vertical axis has its vertex at the origin and passes through point (7, 7). the parabola intersects line y=6 at two points. the length of the segment joining these points is: 14, 13, 12, 8.6, 6.5 .
answer is 14. but i don't understand how it was solved so please try to explain how it solves.
answer is 14. but i don't understand how it was solved so please try to explain how it solves.
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Vertex (0, 0):
h = 0
k = 0
Point (7, 7):
x = 7
y = 7
y = a(x - h)² + k:
7 = a(7 - 0)² + 0
7 = a(7)²
7 = a(49)
7 = 49a
a = 7 / 49
a = 1/7
Equation of Parabola:
y = 1/7 x²
Equation of Line:
y = 6
Point of Intersection: y = y, so
1/7 x² = 6
x² = 6 / (1/7)
x² = 6(7)
x² = 42
x = √42
x = ± 6.48
x1 = 6.48
x2 = - 6.48
Distance = d:
d = x1 - x2
d = 6.48 - (- 6.48)
d = 6.48 + 6.48
d ≈ 13
The distance is 13 units.
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h = 0
k = 0
Point (7, 7):
x = 7
y = 7
y = a(x - h)² + k:
7 = a(7 - 0)² + 0
7 = a(7)²
7 = a(49)
7 = 49a
a = 7 / 49
a = 1/7
Equation of Parabola:
y = 1/7 x²
Equation of Line:
y = 6
Point of Intersection: y = y, so
1/7 x² = 6
x² = 6 / (1/7)
x² = 6(7)
x² = 42
x = √42
x = ± 6.48
x1 = 6.48
x2 = - 6.48
Distance = d:
d = x1 - x2
d = 6.48 - (- 6.48)
d = 6.48 + 6.48
d ≈ 13
The distance is 13 units.
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