Question

If the circle  has the center at  then find a, b.​

Answer 1

Answer:

The tangent is x + y = 1 which is the same as y = -x + 1.

So, gradient of tangent = -1.

We know that radius meets tangent at a right angle.

So, the radius that meets this tangent at the point of contact has gradient -1/-1 = 1.

So, the equation of this radius is :

Find the point of contact of the radius and tangent:

So, (0, 1) lies on the circumference of the circle.

Hence the radius of the circle is:

Hence, the equation of the circle is: