Aryan coordinate challenge #1
Given that two focus of ellipse are
and
and the ellipse touches line
. point of contact of ellipse and line is
. find
.
The answer is 10.5.
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1 solution
see we know in ellipse sum of distance from two focus is constant . now sum of distance of any point from focus on the the ellipse will be less than any point outside. so the question reduces to that find a point on a line such that sum of distances of the point from two fixed points is minimum. we use reflection property of straight line. reflection of (3,5) is (-9,-11).line joining (-9,-11) and (-9,7) intersect the line 3x+4y+21=0 at (-9,1.5)---- 9+1.5=10.5