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Coordinate geometry

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Master | Next Rank: 500 Posts
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by nidhis.1408 » Mon Oct 01, 2012 8:20 am
Given the two lines y = 2x + 5 and y = 2x - 10, what is the area of the largest circle that can be inscribed such that it is tangent to both lines?
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by anuprajan5 » Mon Oct 01, 2012 8:37 am
Hi,

Would the answer be 12.5 pi?

My solution for this is to find x and y intercepts for both lines and then check the distance between these intercepts.

The points that seemed farther seemed to be (0,5) and (5,0). The distance between these is 5 root 2 which becomes the diameter.

Radius - 2.5 root 2.

Area - pi * (2.5 root 2)^2

Regards
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by das.ashmita » Mon Oct 01, 2012 10:40 am
Hi Nidhis



The lines are parallel as the slope is same.

The distance between 2 parallel lines = |C1-C2| / root(m^2 + 1)

= |5-(-10)| / root(2^2 + 1) = 15/root(5) = 3root(5)......diameter of the circle

The radius of the circle = (3root(5))/2

Area = pi * [3root(5))/2]^2 = 11.25pi

Hope its clear :)
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