Triangle ABC is similar to triangle DEF. Find the measure of side DE. Round your
1 answer:
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The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is
The given parameters are:
- Directrices at x = ±2
- Foci at (5, 0) and (−5, 0)
The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:
So, we have:
Evaluate
Hence, the equation of the hyperbola is
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Answer:
l = 2.25 cm
Step-by-step explanation:
given l is inversely proportional to w² then the equation relating them is
l = ← k is the constant of proportion
(i)
to find k use the condition w = 1.5 , l = 16 , then
16 = =
( multiply both sides by 2.25 )
36 = k
l = ← equation of proportion
(ii)
when w = 4 , then
l = =
= 2.25 cm