Question:
Find the distance between the point \( (6, 4\sqrt{3}) \) and the focus of the parabola \( y^2 = 8x \)
Find the distance between the point \( (6, 4\sqrt{3}) \) and the focus of the parabola \( y^2 = 8x \)
Show Hint
The standard focus of a parabola \( y^2 = 4ax \) is at \( (a, 0) \). Use distance formula directly.
Updated On: May 17, 2025
- 64
- 4
- 8
- 2
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The Correct Option is C
Solution and Explanation
Given parabola: \( y^2 = 4ax \Rightarrow 4a = 8 \Rightarrow a = 2 \)
So, focus = \( (a, 0) = (2, 0) \)
Point = \( (6, 4\sqrt{3}) \)
Distance formula:
\[
\begin{align}
\text{Distance} = \sqrt{(6 - 2)^2 + (4\sqrt{3} - 0)^2} = \sqrt{16 + 48} = \sqrt{64} = 8
\]
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