1. Find the equation of the circles which touch the axis of x at a distance of 4 from the origin and cut off an intercept of 6 from the axis of y
  2. A circle having its centre in the first quadrant touches the y axis at a point (0,2) and passes through the point (1,0).Find the equation of the circle 
  3. calculate the co ordinatesof the foot of the perpendicular from the point (-4,2)to the line 3x+2y=5 . find the equation of the smallest circle passing through(-4,2) and having its centre on the line 3x+2y=5        

(1)

The given problem can be represented as given above.

Intercept on y– axis = 6

As circle touches the x– axis at a distance of 4 from the origin, so there are two such circles possible.

E is the mid-point of CD. Join OE, OC and OA.

So, coordinate of centre or point O = (± 4, 5).

Hence, equation of the circle,

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