A circle passes through (-2,4) and touches y axis at (0,2). which one of the following equations can represent a diameter of this circle?

Question

a.2x-3y+10=0 

b.3x+4y-3=0

c.4x+5y-6=0

d.5x+2y+4=0

Answer 1

The answer is the first equation...and here is why.

First draw a sketch to help you decide whether your answers make sense.

First, y=2 is the equation of a diameter since the line perpendicular to a tangent to a circle is a diameter.

The chord between (-2,4) and (0,2) has a slope of -1=(4-2)/(-2-0).

The equation of the chord is -1=(y-2)/2 i.e. y=2-x.

The midpoint of the chord is (-1,3)

The slope of the chord is 1 (negative reciprocal of -1)

The equation of the chord is 1 = (y-3)/(x+1)

The center of the circle is at the intersection of the chord and y=2 and that point is (-2,2)

The only equation which passes through (-2,2) is the first one.

Answer 2

If the circle "touches" the y-axis, the y-axis is tangent to the circle.

The radius/diameter is perpendicular at the point of tangency.

The diameter is on the line y = 2.