Find the shortest distance of the point $(4, 3)$ relative to the ellipse $2 x^{2} + 9 y^{2} = 113$ .

0

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\sqrt{2}

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\sqrt{2} - 1

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\sqrt{2} + 1

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Solution

The correct option is A $0$
Given ellipse is $S : 2 x^{2} + 9 y^{2} - 113$
Now at given point $(4, 3)$ , $S = 2 (4^{2}) + 9 (3^{2}) - 113 = 32 + 81 - 113 = 0$
Clearly given point lie on the ellipse. Hence it's distance relative to given ellipse is zero.

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