Q34 of 63 Page 202

State whether the statements True or False. Justify

The shortest distance from the point (2, –7) to the circle x2 + y2 – 14x – 10y – 151 = 0 is equal to 5.

x2 - 14x + 49 + y2 - 10y + 25 – 74 – 151 = 0


(x – 7)2 + (y – 5)2 = 225


(x – 7)2 + (y – 5)2 = 152


Centre = (7, 5) Radius = 15 units


Putting x = 7 & y = 5 in the circle’s equation,


(7)2 + 52 - 14 (7) – 10 (5) – 151


= -56


-56 < 0


(2, -7) lies inside the circle.


Distance from (2, -7) to (7, 5),


Distance between the point of intersection & centre = [Distance Formula]


D =


D =


D =


D =


Shortest Distance = Radius – Distance between centre & given point


= 15 – 13 = 2 units


Hence the answer is FALSE.


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