Question

If one end of a diameter of a circle 2x² + 2y² -4x -8y +2 = 0 is (-1,2) then the other end of Diameter is :-


a (2,1 )

b ( 3,2)

c ( 4,3 )

d ( 5,4 )

solve with steps :-

Answer 1

hence ans is option b

Answer 2

Equation of the given circle is x2+y2−4x−6y+11=0x2+y2−4x−6y+11=0

Hence the centre of the circle is (2,3)(2,3).

The coordinate of the point which lies on the circle is (3,4)(3,4)

Let the coordinates of the point on the other end of the diameter be (x1,y1)(x1,y1).

The coordinate of midpoint of these two points is (2,3)(2,3)

(ie) x1+32x1+32=2=2

x1=4−3x1=4−3

x1=1x1=1

y1+42y1+42=3=3

∴y1=6−4∴y1=6−4

∴y1=2∴y1=2

Hence the coordinates of the point on the other end of the diameter is (1,2)