The distance of the point (6,4 √3) from the focus of y^2=8 x is

Correct answer: (C) 8. For y^2=8 x (y^2=4 a x ) Focus is (a, 0) ≡(2,0) distance of (6,4 √3) from (2,0)= √((6-2)^2+(4 √3)^2)=√(16+48) =√64 =8

Q92 / 160 · AP EAMCET 2022 (05 Jul Shift 2) · Mathematics

The distance of the point $(6,4 \sqrt{3})$ from the focus of $y^2=8 x$ is

A
$64$
B
$4$
Correct answer
C
$8$
D
$2$

Solution

For $y^2=8 x \quad\left(y^2=4 a x\right)$ Focus is $(a, 0) \equiv(2,0)$ distance of $(6,4 \sqrt{3})$ from $(2,0)=$ $\sqrt{(6-2)^2+(4 \sqrt{3})^2}=\sqrt{16+48}$ $\begin{aligned} & =\sqrt{64} \\ & =8\end{aligned}$

Hence, the correct answer is option: 'C'.

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