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aalokmaths · Apr 30, 2010, 03:23 AM

Find the area of the region included between the circle: x2 + y2 + 2 x + 10y + 27 = 0 and the parabola y2 + 10y – x + 23 = 0

galactus · Apr 30, 2010, 05:19 PM

Check and make sure there is not a typo in the circle equation. Maybe that should be -27?
As is, it has a negative radius which is infeasible.

galactus · May 1, 2010, 10:37 AM

Assuming there was a typo with the circle equation, I am going to go with

$x^{2}+y^{2}+2x+10y-27=0$

Completing the square, we get:

$(x+1)^{2}+(y+5)^{2}=53$

The circle has center at (-1,-5) and has radius $\sqrt{53}\approx 7.28$

Solving this for y, we get:

$y=-\sqrt{-x^{2}-2x+52}-5$ and

$y=\sqrt{-x^{2}-2x+52}-5$

The parabola can be solved for y and we get:

$y=-\sqrt{x+2}-5$

$\sqrt{x+2}-5$

Now, use this info, along with some integration, to find the area.

Please use ^ to designate powers. x2 looks like x times 2.