First slide

Definition of a circle

Question

$x, y \in R satisfies (x + 5)^{2} + (y - 12)^{2} = 14^{2}, then the min value of \sqrt{x^{2} + y^{2}}$

Moderate

A

5
B

3
C

1
D

2

Solution

By parametric equations of a circle, we have
$\begin{array}{l} x + 5 = 14 \cos θ \\ y - 12 = 14 \sin θ \\ \Rightarrow x^{2} + y^{2} = 365 + 28 (12 \sin θ - 5 \cos θ) \\ ∴ m i n i m u m v a l u e o f \sqrt{x^{2} + y^{2}} = \sqrt{365 - 28 (13)} = 1 \end{array}$

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