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Question

# The co-ordinates of the point on the circle x2+y2âˆ’12xâˆ’4y+30=0 which is farthest from the origin are:

A
(9, 3)
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B
(8, 5)
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C
(12, 4)
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D
none of these
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Solution

## The correct option is A (9, 3)Given equation of circle x2+y2−12x−4y+30=0(x−6)2−36+(y−2)2−4+30=0(x−6)2+(y−2)2=10Maximum distance of (0,0) from circle is=√(6−0)2+(2−0)2+√10=2√10+√10=3√10Let coordinates of point P(x1,y1)then √(x1−0)2+(y1−0)2=3√10(1)and this point also satisfies circle(x1−6)2+(y1−2)2=10(2)Solving (1)x12+y12=90(3)Solving (2)x12+y12−12x1−4y1+30=0(4)Solving (3),(4)12x1+4y1−30=9012x1+4y1=1203x1+y1=30(5)Equation of line passing through origin, center and point (x1,y1) is(y−0)=(26)(x−0)3y=xPoint (x1,y1) also lies on this line3y1−x1=0(6)Solving (5),(6)3x1+y1=309y1−3x1=0¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯10y1+0=30⇒y1=3,x1=9The point (x1,y1) is (9,3)

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