circle inscribed in ellipse

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}}

3 Answers

11
Mani Pal Singh ·

method

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

62
Lokesh Verma ·

you have to minimize (4 cosα-1)2+ 4sin2α

1
The Scorpion ·

Equation 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... :)

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