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Find the minimum length of radius vector...

Find the minimum length of radius vector of the curve `(a^2)/(x^2)+(b^2)/(y^2)=1`

Text Solution

Verified by Experts

The correct Answer is:
|a+b|
`(a^(2))/(x^(2))+(b^(2))/(y^(2))=1`
Let x =`r cos phi , y =r sin phi`
`therefore = (a^(2))/(r^(2)cos^(2)phi)+(b^(12))/(r^(2)sin^(2)phi)=1`
`therefore a^(2) sec^(2)phi tan phi =b^(2) cosec^(2) phi cot phi`
`therefore tan^(4)phi=(b^(2))/(a^(2))`
`therefore r^(2)min =a^(2)1+(b)/(a)+b^(2)(1+(a)/(b))=(a+b)^(2)`
`therefore r_(min) =|a+b|`
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