Two circles of radius 6 are tangent to the graph of y2 = 4x at the point (1, 2). Find equations of these two circles.

Question

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Answer 1

Determine slope of tangents at the point (1, 2)

Calculate negartive reciprocals of slopes. These are slopes of diameters of circle.

Determine equations of diameters of circles using slopes asnd (1, 2)

Determine point in diameters 6 units from (1, 2). These are the centers.

Determine equation of circles using centers and r².