Parametrics (3 unit Maths) Help (1 Viewer)

[atar90plus]

Could you guys please help me with these questions. I am pretty bad with parametrics at the moment (trying to review) with only getting just above half of the total parametrics questions correct in my prelim. I done most of them already but just got stuck in parts of the question

4. Find the equation of the tangent to the parabloa x^2=-2y which is parallel to the line 2x+3y-5=0 and also find the point of contact between this line and the parabola. Answer: y=-2/3x +2/9, (2/3, -2/9)

For the first part of the question (equation of tangent) I got y=-2/3x +10/3 so I am not sure if my expansion/calculations are off or if the answer is wrong. I do not know how to find the POC though

6. P(2ap,ap^2) and Q(2aq,aq^2) are two points on the parabola x^2=4ay

c) If S is the focus of the parabola, prove that : 1/SP +1/SQ =1/a

7. Two points P(2AP,Ap^2) and Q(2Aq,Aq^2) lie on the parabola x^2=4Ay, where A<0. The chord PQ passes through the focus.

c) Show that the chord PQ has length A(p+1/p)^2

 

[HeroicPandas]

Could you guys please help me with these questions. I am pretty bad with parametrics at the moment (trying to review) with only getting just above half of the total parametrics questions correct in my prelim. I done most of them already but just got stuck in parts of the question

4. Find the equation of the tangent to the parabloa x^2=-2y which is parallel to the line 2x+3y-5=0 and also find the point of contact between this line and the parabola. Answer: y=-2/3x +2/9, (2/3, -2/9)

For the first part of the question (equation of tangent) I got y=-2/3x +10/3 so I am not sure if my expansion/calculations are off or if the answer is wrong. I do not know how to find the POC though

6. P(2ap,ap^2) and Q(2aq,aq^2) are two points on the parabola x^2=4ay

c) If S is the focus of the parabola, prove that : 1/SP +1/SQ =1/a

7. Two points P(2AP,Ap^2) and Q(2Aq,Aq^2) lie on the parabola x^2=4Ay, where A<0. The chord PQ passes through the focus.

c) Show that the chord PQ has length A(p+1/p)^2

I will scan my solution TO question 6 and 7

 

[HeroicPandas]

Q6 and Q7 please ZOOM...

 

[zeebobDD]

to find point of contact solve the two equations of the parabola and the equation of the tangent simultaneously

 

[atar90plus]

Thanks

to find point of contact solve the two equations of the parabola and the equation of the tangent simultaneously

 

[HeroicPandas]

Did u even view my solutions for q6/7...?

 

[atar90plus]

Yes. Oh sorry thought I said thanks to both users that reply. For some reason it did not appear.

Did u even view my solutions for q6/7...?

 

[atar90plus]

But I really thank you so much for the worked solutions. Sorry about that

 

[HeroicPandas]

But I really thank you so much for the worked solutions. Sorry about that

no probs