Question:
The foci of a hyperbola are (8,3) and (0,3) and eccentricity is $4/3$. Then the length of the transverse axis is:
The foci of a hyperbola are (8,3) and (0,3) and eccentricity is $4/3$. Then the length of the transverse axis is:
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Always identify if the transverse axis is horizontal or vertical. Here, $y=3$ is constant, so it is horizontal.
Updated On: Apr 20, 2026
- $32/3$
- 4
- 8
- $8/3$
- 6
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The Correct Option is
Solution and Explanation
Step 1: Understanding the Concept:
In a hyperbola, the distance between the foci is $2ae$, where $a$ is the length of the semi-transverse axis.
Step 2: Key Formula or Approach:
Distance between foci $= 2ae$.
Length of transverse axis $= 2a$.
Step 3: Detailed Explanation:
Foci: $(8, 3)$ and $(0, 3)$.
Distance $= 8 - 0 = 8$ (horizontal).
So, $2ae = 8$.
Given $e = 4/3$.
$2a \times (4/3) = 8$
$2a = 8 \times (3/4) = 6$.
The length of the transverse axis is $2a = 6$.
Step 4: Final Answer:
The length of the transverse axis is 6.
In a hyperbola, the distance between the foci is $2ae$, where $a$ is the length of the semi-transverse axis.
Step 2: Key Formula or Approach:
Distance between foci $= 2ae$.
Length of transverse axis $= 2a$.
Step 3: Detailed Explanation:
Foci: $(8, 3)$ and $(0, 3)$.
Distance $= 8 - 0 = 8$ (horizontal).
So, $2ae = 8$.
Given $e = 4/3$.
$2a \times (4/3) = 8$
$2a = 8 \times (3/4) = 6$.
The length of the transverse axis is $2a = 6$.
Step 4: Final Answer:
The length of the transverse axis is 6.
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