Solve the problem.
-Find the shortest distance from the origin to a point on the circle defined by $$x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }$$
A) $2 \sqrt { 130 } - + 3$
B) $\sqrt { 130 } + 3$
C) $\sqrt { 130 } - 3$
D) $2 \sqrt { 130 } - 3$

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the form $(x - 7)^2 + (y - 9)^2 = 25$, which represents a circle with center (7, 9) and radius 5. The shortest distance from the origin (0, 0) to the circle is the distance from the origin to the center minus the radius: $\sqrt{7^2 + 9^2} - 5 = \sqrt{130} - 5$.

Solve the Problem x2+y2−14x−18y+121=0. x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }x2+y2−14x−18y+121=0.

Solve the Problem $x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }$