The normal at a variable point \( P \) on ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \...

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The normal at a variable point \( P \) on ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \), \( (ab) \) meets axes of the ellipse in \( Q \) and \( R \). Then which of the following is/are correct statement(s)
(a) The locus of mid-point of \( Q R \) is ellipse
(b) The locus of mid-point of \( Q R \) is conic whose eccentricity is same as of given ellipse
(c) The locus of mid-point of \( Q R \) is hyperbola
(d) The locus of mid-point of \( Q R \) is conic with its eccentricity half of the eccentricity of given ellipse
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