Question

Prove or disprove that the circle with equation x^2-4x+y^2=-3 intersects the y axis

Answer 1

The general equation given is x^2 - 4x + y^2 = -3. Transform this to an equation of a circle of the form x^2 + y^2 = r^2.

Use completing the square method:

x^2 - 4x + 4 + y^2 = -3 + 4
(x - 2)^2 + y^2 = 1

the center of the circle is (2,0) and r = 1

To check if it intersects the y axis, find the value of the x-intercept.