Find the eqtn of d circle if d circle is tan to d line x+2y=3 at the point (-1,2) & d center is on d y-axis.?

Question

"Find the equation of the circle if the circle is tangent to the line x+2y=3 at the point (-1,2) and the circle is on the y-axis."

Another analytic geometry homework..I don't know what equation will use....

"Find the equation of the circle if the circle is tangent to the line x+2y=3 at the point (-1,2) and the center is on the y-axis."

I'm sorry for the typographical error on the question above..It is not "the circle is on the y-axis", it is "the center is on the y-axis". thanks...

Answer 1

If the line is tangent to the circle @ (-1,2), the radius will be perpendicular to the line at that point, and will have a slope of 2:
(y - 2) / (x + 1) = 2
y = 2x + 4
y(0) = 4
x^2 + (y - 4)^2 = r^2
r^2 = 1 + 4 = 5
x^2 + (y - 4)^2 = 5

Answer 2

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