parametric equations (1 Viewer)

maths lover · Sep 2, 2011

p(2ap,ap^2) and q(2aq,aq^2) are variable points on the parabola x^2=4ay. so that angle pqr=90. the tangents at p and q meet at t. find the locus of t.
i know the process of doing these types of question i got up to
0=x(p-q)-a(p^2-q^2) and i know that you will end up getting that pq=something but i just can seem to get rid of the parameters.

rolpsy · Sep 2, 2011

$\begin{align*} m_{p}&=p,\ m_{q}=q\\ m_{p} &\perp m_{q}\\ \therefore pq&=-1 \end{align*} \\ \begin{cases} y&=px-ap^2\\ y&=qx-aq^2\\ \end{cases}\\ \begin{align*} \therefore px-ap^2&=qx-aq^2\\ x(p-q)&=a(p+q)(p-q)\\ x&=a(p+q) \\\\ y&=p\left [ a(p+q) \right ]-ap^2\\ &=ap^2+apq-ap^2\\ &=apq\\ &=-a \textup{ .. as }pq=-1 \end{align*}$

so T moves along the directrix

maths lover · Sep 3, 2011

thanks so much

parametric equations (1 Viewer)

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