HardMathematicsHigh School (11–12)Coordinate Geometry › Circles and Conic SectionsNumerical

A focal chord PQ of the parabola y² = 12x has its end P at the parameter t = 2…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A focal chord $PQ$ of the parabola $y^2 = 12x$ has its end $P$ at the parameter $t = 2$ . Find the length of the focal chord, the distance of $P$ from the focus, and the distance of $Q$ from the focus.

Need a reminder? The key ideaShow

A focal chord has ends at $t$ and $-\dfrac{1}{t}$ and length $a\left(t + \dfrac{1}{t}\right)^2$ . Also $\dfrac{1}{SP} + \dfrac{1}{SQ} = \dfrac{1}{a}$ . A ray parallel to the axis reflects through the focus.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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