Question

Find the area of the region satisfying the inequality x^2 + y^2 <= 4x + 6y+13

Answer 1

26pi

Explanation:

We are given a region satisfied by the equation as

`x^2 + y^2 <= 4x + 6y+13`

Rewrite this on left side and use completion of squares method

`x^2-4x+y^2-6y-13\leq 0\\(x-2)^2+(y-3)^2\leq 26`

Thus the region is the interior of a cricle with centre at (2,3) and radius = square root of 26

Hence area = area of a circle

=
`\pi r^2 =26\pi`