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... :)
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
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