An ellipse given by x^2+4y^2=16 has a circle inscribed with centre at (1,0) ,what is the maximum possible radius?
Ans:\sqrt{\frac{11}{3}}
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3 Answers
11method
iss ellipse ka a=4 and b=2 hai
circle ki eq
(x-1)2+y2=r2 hai
take a point on ellipse (x,y)
find the point where they meet
now
AT THE POINT OF TOUCH DRAW A TANGENT TO THE CIRCLE AT (x,y)
IT WOULD BE THE TANGENT OF ELLIPSE ALSO
EQUATE TO GET (x,y)
THE DISTANCE OF THE TANGENT FROM CENTER IS THE RADIUS
1Equation of normal to an ellipse in slope-form...
y = mx \pm \frac{m(a^{2}-b^{2})}{\sqrt{a^{2}+b^{2}m^{2}}}
this will minimize calculations...!!!
hope it helps... :)