Question

If point P(x,y)is situated on that circle whose centre is (3,-2) and radius is 3unit then find x and y

Answer 1

The values will be x² + y² = 6x - 4y - 4

Point on the circle = P(x,y) (Given)

Centre of the circle = (3, -2) (Given)

Radius of the circle = a =  3 units (Given)

The equation of circle when centre (g,f) and with given radius will be -

(x - g)² + (y - f)² = a²

Where g = 3, f = -2,

Using the equation - (a+b)² = a² + b² + 2ab

Putting values in equation, we have

(x - 3)² + (y + 2)² = 3²

x²- 6x + 9 + y² + 4y + 4 = 9

x² + y² - 6x + 4y + 13 = 9

x² + y²- 6x + 4y + 13 - 9 = 0

x² + y² - 6x + 4y + 4 = 0

x² + y² = 6x - 4y - 4