Question

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. X2 (y â€"" 3)2 = 36 x2 (y â€"" 5)2 = 6 (x â€"" 4)² y² = 36 (x 6)² y² = 144 x2 (y 8)2 = 36.

Answer 1

The general equation of a circle is $(x-h)^2+(y-k)^2=r^2$. The two options are option(A) and option(E).

Given,

There are five options in which five equation of the circle is given.

We have to find the two equations of the circle which have the diameter of 12 units and its center lies on the y-axis.

The general equation of circle.

the general equation of circle having radius of r units and (h,k) as center of circle is given as,

$(x-h)^2+(y-k)^2=r^2$

We also know that for the center to lie on y-axis, the value of h becomes 0.

So, the equation will be,

$(x)^2+(y-k)^2=r^2$

Now, it is clear from all the options that option(A) option(C) and option(E) has radius of 6 units, so neglecting all the other options.

Clearly, in option(c) the center doesn't lie on the y-axis.

so this can't be the required equation.

Therefore, the two options will be option(A) and option(E).

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