Question: Find the equation of the circle whose centre is (-2,5) and radius 17 units.


Solution:
Given,
In a circle,
Centre (h,k) = (-2,5)
Radius (r) = 17 units

Using formula of circle equation,
$ \sqrt{(x - h)^2 + (y - k)^2} = r$
$or, (x - h)² + (y - k)² = r²$
$or, \{x - (-2)\}^2 + (y - 5)^2 = 17^2$
$or, (x +2)^2 + y^2 - 10y +25 = 289$
$or, x^2 + 4x +4 + y^2 - 10y = 264$
$or, x^2 + y^2 + 4x -10y - 260 = 0$ is the required equation.

Therefore, the required equation of that circle is x² +y² +4x -10y -260 = 0.

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