Most Important Selected Qs for JEE AdvancedMathematicsEllipse

Find the value of k for which the point P(2, k) on the ellipse x^2+2 y^2=6 , which is nearest to the line x+y=7 .

Correct answer

Step-by-step solution

The given equation can be written as x^2 6 + y^2 3 =1 , which represents an ellipse. Any point on this ellipse is P ( 6 , 3 ) . The shortest distance between the ellipse and the given line is along the common normal to both. Slope of the normal at P is 6 3 cosec = 2 =1 slope of normal to the line x+y=7 Hence = 2 3 , = 1 3 so that P is (2,1) .

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