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Find the minimum distance of any point o...

Find the minimum distance of any point on the line `3x+4y-10=0` from the origin using polar coordinates.

Text Solution

Verified by Experts

The correct Answer is:
2 units
Let the polar coordinates of any point on the curve be `P(r,theta)`. Then its cartesian coordinates are `P(rcostheta,rsintheta)`.
P lies on the line. Therefore,
`3rcostheta+4rsintheta-10=0`
or `r=(10)/(3costheta+4sintheta)`
Now, `(3costheta+4sintheta)_(max)=5`
`therefore r_(min)=(10)/(5)=2`
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