We have
The equation of the tangent is , where are the coordinates of P.
Therefore,
Then
We have
From the first equation . Replace p in the second:
P(2ap, ap^2) is a point on the parabola x^2 = 4ay. T is the foot of the perpendicular from P to the x-axis. R is the point where the tangent at P crosses the axis of the parabola. M is the midpoint of RT. Show that the locus of M is x^2 = -2ay
I'm having SO much trouble on this question, ive tried so many ways but they never come to that equation
I worked out that the co-ordinates of point R are (0,y) and T (2ap,0)
I then went and figured out the m(RT) and then the equation of RT.
m(RT) = -y/2ap
Then I worked out the midpoint of RT, M which was (ap, y/2)
but i am stuck on what to do next, i tried a few different approaches and they all didnt work, am i even going in the right direction?? T.T""
please helpp me !
thankyou =)