Question

If a be the radius of circle which touch x-axis at origin then find equation of circle

Answer 1

Answer:

X² + Y² + a - 2.a.(Xcosx-Ysinx) = a²

Step-by-step explanation:

Refer to the attachment for diagram.

According to the diagram,

distance of centre from y axis = a cosx

distance of centre from x axis = a sinx

Thus, coordinates of centre is, (a cosx, a sinx)

Now, equation of circle =

(X-a)² + (Y-b)² = r²

(X- a cosx)² + (Y-a sinx)² = a²

X² + a²cos²x - 2.X.acosx + Y² + a²sin²x - 2.Y.asinx = a²

X² + Y² + a.( sin²x + cos²x ) - 2.a.(Xcosx-Ysinx) = a²

X² + Y² + a - 2.a.(Xcosx-Ysinx) = a²

I hope this is the answer. If u want a more simplified answer, just continue with the above last step..

I HOPE U UNDERSTOOD  !!