Parametrics Help (1 Viewer)

[atar90plus]

Could you guys please help me with these questions. There are no answers so I am just assuming that I got it wrong due to my knowledge on parametrics is not that strong yet

16. For the parabola x^2=4ay with points P(2ap,ap^2) and Q(2aq,aq^2)

b) Show that q approaches p the equation of the chord becomes the equation of the tangent

17. On a diagram shows the points P(2ap,ap^2) and Q(2aq,aq^2) on the parabola x=2t and y=t^2 where p is not equal to q

ii) The chord PQ has a gradient "m" and passes through the point A(0,-2). Find in terms of "m", the equation of PQ and hence show that p and q are the roots of the equation t^2 -2mt+2=0

iii) By considering the sum and product of the roots of this quadratic equation, show the point r lies on the original parabola

19. At the distinct points P(2at, at^2) and Q (2au,au^2) on the prabola x^2=4ay, the tangents are drawn

ii) From the point R(a,-6a) two tangents are drawn to the parabola x^2=4ay. If the points of contact of these tangents are P and Q, show that the triangle PQR is isosceles

 

[Come at me]

i know but srsly cbf typing ...idk how to use latex

 

[Sy123]

Could you guys please help me with these questions. There are no answers so I am just assuming that I got it wrong due to my knowledge on parametrics is not that strong yet

16. For the parabola x^2=4ay with points P(2ap,ap^2) and Q(2aq,aq^2)

b) Show that q approaches p the equation of the chord becomes the equation of the tangent

17. On a diagram shows the points P(2ap,ap^2) and Q(2aq,aq^2) on the parabola x=2t and y=t^2 where p is not equal to q

ii) The chord PQ has a gradient "m" and passes through the point A(0,-2). Find in terms of "m", the equation of PQ and hence show that p and q are the roots of the equation t^2 -2mt+2=0

iii) By considering the sum and product of the roots of this quadratic equation, show the point r lies on the original parabola

19. At the distinct points P(2at, at^2) and Q (2au,au^2) on the prabola x^2=4ay, the tangents are drawn

ii) From the point R(a,-6a) two tangents are drawn to the parabola x^2=4ay. If the points of contact of these tangents are P and Q, show that the triangle PQR is isosceles

16b) I dont know how thats a question because it is painfully obvious that its a tangent if P and Q are the same point, but for computational reasoning:




17. Im assuming that the parametric equations are 2p p^2 and 2q q^2 rather than them ahving an a in there.

ii)

This line indeed intersects the parabola with parametric equations x=2t y=t^2, subbing them in:



iii) THere is no 'r'? you must of forgotten something


Please post the whole questions scan them or something