Skip to content

Course home

Sign up

1 Pure Mathematics

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497
Question 81

A curve C C\,C has the equation

xy2+x2y=10xy^2 + x^2y = 10xy2+x2y=10

a.

Prove that C C\,C does not intersect the coordinate axes.

[2]
b.

Show that

dydx=−y(2x+y)x(x+2y)\displaystyle \frac{dy}{dx} = -\frac{y(2x + y)}{x(x + 2y)}dxdy​=−x(x+2y)y(2x+y)​

[4]
c.

Find the exact coordinates of the stationary point of CCC.

[2]
Markscheme

1 Pure Mathematics Questions

  1. A Level
  2. /Maths
  3. /1 Pure Mathematics

Question bank