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1326	Let a, r, s, t be non-zero real numbers. Let P(at², 2at), Q, R(ar², 2ar and S(as², 2as) be distinct points on the parabola y² = 4ax. Suppose PQ is the focal chord and QR and PK are parallel, where K is point (2a, 0)If st = 1 then the tangent at P and normal at S to the parabola meet at a point whose ordinate is a) $\frac{{(t^{2} + 1)}^{2}}{2 t^{3}}$ b) $\frac{a {(t^{2} + 1)}^{2}}{2 t^{3}}$ c) $\frac{{a (t^{2} + 1)}^{2}}{r^{3}}$ d) $\frac{{a (t^{2} + 2)}^{2}}{r^{3}}$ Let a, r, s, t be non-zero real numbers. Let P(at², 2at), Q, R(ar², 2ar and S(as², 2as) be distinct points on the parabola y² = 4ax. Suppose PQ is the focal chord and QR and PK are parallel, where K is point (2a, 0)If st = 1 then the tangent at P and normal at S to the parabola meet at a point whose ordinate is a) $\frac{{(t^{2} + 1)}^{2}}{2 t^{3}}$ b) $\frac{a {(t^{2} + 1)}^{2}}{2 t^{3}}$ c) $\frac{{a (t^{2} + 1)}^{2}}{r^{3}}$ d) $\frac{{a (t^{2} + 2)}^{2}}{r^{3}}$	IIT 2014
1327	The tangent PT and the normal PN of the parabola y² = 4ax at the point P on it meet its axis at the points T and N respectively. The locus of the centroid of the triangle PTM is a parabola whose a) Vertex is $(\frac{2 a}{3}, 0)$ b) Directrix is x = 0 c) Latus rectum is $\frac{2 a}{3}$ d) Focus is (a, 0) The tangent PT and the normal PN of the parabola y² = 4ax at the point P on it meet its axis at the points T and N respectively. The locus of the centroid of the triangle PTM is a parabola whose a) Vertex is $(\frac{2 a}{3}, 0)$ b) Directrix is x = 0 c) Latus rectum is $\frac{2 a}{3}$ d) Focus is (a, 0)	IIT 2009

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