Let the tangents at points P and Q on the ellipse x^ 2 /2 + y^ 2 /4 = 1 meet at the point R( 2 , 2 2 - 2). If S is the focus of the ellipse on its negative major axis, then SP^ 2 + SQ^ 2 is equal to _____.

JEE Main 2022 Mathematics question

Let the tangents at points P and Q on the ellipse meet at the point , ). If S is the focus of the ellipse on its negative major axis, then is equal to .

Answer: 13

Solution

The tangent of slope m to the ellipse is y = mx . It passes through , ): , which leads to together with the vertical tangent . So the

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Question ID VK-034708