Parametric (1 Viewer)

[ngogiathuan]

I got stuck at question 18 page 337 from cambridge book
"Show that the common chord of any two circles having focal chords of x^2=4ay as diameters passes through the vertex of the parabola. (You may assume that tangents at the extremities of a focal chord are perpendicular)"

Anyone knows how to do that

 

[ianc]

okay the hardest thing here is the diagram.....

also, are you sure you trancribed the question exactly? if so, it is very badly worded. anyway, here goes.


Obviously it is a parabola question, so let's draw a parabola.

Next, it mentions 2 circles with their diameters being focal chords. So, first I drew 2 focal chords (one red, one blue) and then circles around them such that the focal chords are now the diameters of the circles.

Here it gets messy. What we need to prove is that the common chord (that huge chunky green line down the middle) passes through the parabola's vertex - ie (0,0)

I also drew in green the other piece of infomation they give us: the tangents to the circles at their diameters are perpendicular (well, they kind of look that way on the diagram )

I am assuming that your issue was just wondering wtf the question was asking - i hope my dodgy paint diagrams have helped you understand. if you still need help with doing the rest of the question (because it does look like a tricky one), please ask.

 

[ngogiathuan]

Well, to be honest, I really really don't know how to prove this things here. I tried writing down the equations of that 2 circles and the equation of that stupid line, but things got complicated and I gave up.
I really appreciate if you could help me with that question

 

[ngogiathuan]

Can anyone help me? I still don't know how to do it

 

[jyu]

I got stuck at question 18 page 337 from cambridge book
"Show that the common chord of any two circles having focal chords of x^2=4ay as diameters passes through the vertex of the parabola. (You may assume that tangents at the extremities of a focal chord are perpendicular)"

Anyone knows how to do that

http://imageshack.us

 

[steffiduck]

I got stuck at question 18 page 337 from cambridge book

I'm stuck on Q19+ in the Cambridge book, and the teachers have no idea how to do q19. If anyone knows how to do it, help would be greatly appreciated

thanks

stef

 

[pLuvia]

Mind if you post the question up for people to actually try and solve it?