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Analytical Geometry

Cool goIITian

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3 Mar 2010 13:22:24 IST

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Circles-find the area of a circle given the eq of circle is x=3+4cos? , y=5+4sin?

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Circles-find the area of a circle given the eq of circle is x=3+4cosφ , y=5+4sinφ

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monica

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Joined: 7 Feb 2010

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3 Mar 2010 13:48:30 IST

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equation of the circle is (x-3)^2+(y-5)^2=16 u hav centre (3,5) and radius 4 so area is pi(r^2) so ans is 16pi

Deepak Aggarwal

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Joined: 9 May 2009

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4 Mar 2010 09:52:45 IST

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x = 3 + 4cosφ

or, cosφ = (x - 3) / 4

squaring both sides, cos²φ = (x - 3)² / 16 ----- (1)

SImilarly, sin²φ = (y - 5)² / 16 ---- (2)

Adding, (1) and (2), (x - 3)² + (y - 5)² = (4)²

which is the equation of circle with centre (3,5) and radius 4 units.

So, area of circle = π(4)² = 16π square units (Ans)............

edison

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Joined: 19 Oct 2006

Posts: 7452

25 Feb 2011 16:57:39 IST

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It is parametric equation for cirlce.

Now,

y=5+4sinφ

x = 3 + 4cosφ

Thus cos²φ + sin²φ = 1

or (x - 3)² / 16 + (y - 5)² / 16 = 1

or (x - 3)² + (y - 5)² = 16 = 4²

Thus radius of the circle = 4 units

So area = A = Pi r² = 16 Pi

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