<span>The sinusoidal curves are shown in the picture attached.
Note that the two waves have the same amplitude (same "height"), the same wavelength (same distance from one peak to the next one) and therefore the same frequency, but different phase (they start in different points).
When you sum two different sinusoidal curves with the same amplitude and frequency, but different phase you get a sinusoidal wave with the same frequency as the original curves, but a different amplitude and a different phase.
Therefore, the correct answer is
graph B).
</span>
Answer:
C
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant.
Using the distance formula
= | y - 5 |
Squaring both sides
(x - 4)² + (y - 1)² = (y - 5)² ← distribute the factors in y
(x - 4)² + y² - 2y + 1 = y² - 10y + 25 ( subtract y² - 10y + 25 from both sides )
(x - 4)² + 8y - 24 = 0 ( subtract (x - 4)² from both sides )
8y - 24 = - (x - 4)² ← add 24 to both sides )
8y = - (x - 4)² + 24 ( divide both sides by 8 )
y = -
(x - 4)² + 3
Hence
f(x) = -
(x - 4)² + 3 → C