P is a point on the locus of the $$mid-points$$ of thechords of the parabola $$y2=4ax$$ passing throughthe vertex of the parabola; S is the focus of theparabola and the line joining S and P is producedto meet the parabola at Q. If the ordinate of P isequal to its abscissa, coordinates of Q are

Question

P is a point on the locus of the $$mid-points$$ of thechords of the parabola $$y2=4ax$$ passing throughthe vertex of the parabola; S is the focus of theparabola and the line joining S and P is producedto meet the parabola at Q. If the ordinate of P isequal to its abscissa, coordinates of Q are

Infinity Learn · Accepted Answer

$$O(0$$, $$0)$$ is the vertex and $$Rat2$$,$$2at$$ is any pointon the parabola. $$at2/2$$,$$2at/2$$ is the $$mid-point$$ ofthe chord OR. Whose locus is $$y2=2ax$$ coordinatesof P on this locus are (2a$$, $$2a), focus is $$S(a$$, $$0)$$. Equation of SP is $$y=2(x$$−$$a)$$ which $$meetsy2=4ax$$ at the point Q for which  $$4(x$$−$$a)2=4ax$$⇒$$x2$$−$$3ax+a2=0$$ which is not satisfied by thepoints in (a), (b) or (c).

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P is a point on the locus of the mid-points of thechords of the parabola y2=4ax passing throughthe vertex of the parabola; S is the focus of theparabola and the line joining S and P is producedto meet the parabola at Q. If the ordinate of P isequal to its abscissa, coordinates of Q are

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