isi-entrance 2013 Q48

isi-entrance · India 4 marks Straight Lines & Coordinate Geometry Locus Determination

Let $L$ be the point $(t, 2)$ and $M$ be a point on the $y$-axis such that $LM$ has slope $-t$. Then the locus of the midpoint of $LM$, as $t$ varies over all real values, is
(A) $y = 2 + 2x^2$
(B) $y = 1 + x^2$
(C) $y = 2 - 2x^2$
(D) $y = 1 - x^2$

Let $L$ be the point $(t, 2)$ and $M$ be a point on the $y$-axis such that $LM$ has slope $-t$. Then the locus of the midpoint of $LM$, as $t$ varies over all real values, is\\
(A) $y = 2 + 2x^2$\\
(B) $y = 1 + x^2$\\
(C) $y = 2 - 2x^2$\\
(D) $y = 1 - x^2$

Paper Questions

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