Area of circle, Lol

Geometry Level 5

P ≡ 16 x 2 − 24 x y + 9 y 2 − 180 x + 10 y + 625 \large P \equiv 16x^{2} - 24xy + 9y^{2} - 180x +10y + 625

If the center of a circle lies on latus rectum of the conic P = 0 P=0 and the directrix of the conic P = 0 P=0 is the tangent to this circle, then find the area of this circle.


The answer is 12.566370.

Surya Prakash by Surya Prakash , 22, India

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1 solution

汶良 林
Oct 7, 2015

The center of the circle lies on the focus of the conic P = 0 ?

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You should prove that how.

Surya Prakash - 5 years, 8 months ago

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The center of the circle lies on the conic P = 0, it can be anywhere of the conic, so it would not have a certain answer!

汶良 林 - 5 years, 8 months ago

Is there any short approach to the problem . i simply assumed the focus to be (a,b) , eccentricity to be e , equation of directrix to be cx+dy+f = 0 and applied general equation of conic . then i compared that stupid long equation with this to get the values of a,b,e,c,d,f .but thats a lot of work (although the calculations are very simple everything cancels so fine)

pankaj gupta - 5 years, 6 months ago

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