A line bisecting the ordinate PN of a point P (at2$$ , $$2at), t $$0$$, on the parabola $$y2$$ $$=$$ $$4ax$$ is drawn parallel to the axis to meet the curve at Q. If NQ meets the tangent at the vertex at the point T, then the coordinates of T are.

Question

A line bisecting the ordinate PN of a point P (at2$$ , $$2at), t > $$0$$, on the parabola $$y2$$ $$=$$ $$4ax$$ is drawn parallel to the axis to meet the curve at Q. If NQ meets the tangent at the vertex at the point T, then the coordinates of T are.

Infinity Learn · Accepted Answer

Equation of the line parallel to the axis and bisecting the ordinate PN of the point P (at2$$ , $$2at) is y $$=at$$ which meets the parabola $$y2$$ $$=$$ $$4ax$$ at the point $$Qat24$$,at Coordinates of N are (at2$$ , $$0). Equation of NQ is $$y=0$$−$$atat2$$ $$at2/4x$$−$$at2which$$ meets the tangent at the vertex, x $$=$$ $$0$$, at the point y $$=$$ $$4at/3$$.

A line bisecting the ordinate $P N$ of a point $P (a t^{2}, 2 a t), t > 0,$ on the parabola $y^{2} = 4 a x$ is drawn parallel to the axis to meet the curve at $Q$ . If $N Q$ meets the tangent at the vertex at the point T, then the coordinates of T are.

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A line bisecting the ordinate PN of a point P (at2 , 2at), t > 0, on the parabola y2 = 4ax is drawn parallel to the axis to meet the curve at Q. If NQ meets the tangent at the vertex at the point T, then the coordinates of T are.

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A line bisecting the ordinate $P N$ of a point $P (a t^{2}, 2 a t), t > 0,$ on the parabola $y^{2} = 4 a x$ is drawn parallel to the axis to meet the curve at $Q$ . If $N Q$ meets the tangent at the vertex at the point T, then the coordinates of T are.