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Question:

A circle passes through (-2,4) and touches the y-axis at (0,2). Which one of the following equations can represent a diameter of this circle? 2x-y+10=0, 4x+5y-6=0, 5x+2y+4=0, 3x+4y-9=0

2x-y+10=0

5x+2y+4=0

3x+4y-9=0

4x+5y-6=0

Solution:

(-2,4) and touches the y-axis at (0,2)
Radius of circle = 2 units
From the figure we can see that (-2,4) is the end point of diameter whose other end is (-2,0).
So, centre of this circle is (-2,2).
By substituting the point (-2,2) in the equations given in the options, we can see that, only 2x-y+10=0 passes through (-2,2).