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Question
The equation of the circle whose radius is 5 and which touches the circle x2+y2−2x−4y−20=0 externally at the point (5, 5), is
The equation of the circle whose radius is 5 and which touches the circle x2+y2−2x−4y−20=0 externally at the point (5, 5), is
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Solution
The correct option is B
Let the centre of the required circle be (x1,y1) and the centre of given circle is (1, 2). Since radii of both circles are same, therefore, point of contact (5, 5) is the midpoint of the line joining the centres of both circles. Hence x1=9 and y1=8. Hence the required equation is (x−9)2+(y−8)2=25
⇒x2+y2−18x−16y+120=0
Tick: the point (5, 5) must satisfy the required circle. Hence the required equation is given by (b).
Let the centre of the required circle be (x1,y1) and the centre of given circle is (1, 2). Since radii of both circles are same, therefore, point of contact (5, 5) is the midpoint of the line joining the centres of both circles. Hence x1=9 and y1=8. Hence the required equation is (x−9)2+(y−8)2=25
⇒x2+y2−18x−16y+120=0
Tick: the point (5, 5) must satisfy the required circle. Hence the required equation is given by (b).
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