A bit of help please! (1 Viewer)

[Makematics]

Hey guys, so these two questions have stumped me. It would be great if you could help me out

1. Find the co-ordinates of the foci of the ellipse whose equation is: 25(x-1)^2 + 16y^2=100
I tried doing it, but got something different to their answer, which is (1,3/2) and (1,-3/2)

2. AB is any chord of a circle of centre O. Another chord XY is drawn to pass through P, the midpoint of AB. Tangents at X and Y are drawn to meet AB or BA produced at M and N respectively. Prove that AM=BN.

 

[integral95]

For Q 1 lol.

Is there are diagram for your 2nd question?

 

[HeroicPandas]

 

[Makematics]

View attachment 28694
For Q 1 lol.

Is there are diagram for your 2nd question?

Ok lol thanks. Fack i made a silly mistake in my solution at first -.- anyways nah, no diagram. It shouldnt be too hard to draw up though

 

[Makematics]

Bump for circle geo question!

 

[HeroicPandas]

did u get my PM?

 

[Makematics]

did u get my PM?

Yep, replied just then thanks!

 

[Drongoski]

Circle Geometry Question

AB is any chord of a circle, centre O. Another chord XY is drawn to pass thru P, the mid-point of AB. Tangents at X and Y are drawn to meet AB or BA produced to meet at M and N respectively. Prove that AM = BN.

Maybe Heroic can supply the diagram.


Proof Outline:

Let the other tangent to the circle (touching at Z) from M meet the tangent to the circle at Y, viz NY produced, at point R.

Now angle ROZ = angle ROY (since triangles ROZ and ROY are congruent)

.: angle ZOP (=180 - angle ROZ) = angle YOP (180 - angle ROY)

Now OPMZ is cyclic (since opp angles OPM & OZM are 90: OP is perpendicular to AB)

And OPNY is cyclic (similarly)

.: angle ZMP (= 180 - angle ZOP) = angle YNP(180 - angle YOP)

.: triangle RMN is isosceles with RM = RN

.: RP, being perpendicular to MN, bisects MN.

.: MP = PN

But AP = PB (since perp. from centre O to chord AB, bisects it)

.: MP - AP = PN - PB

i.e. AM = BN

QED (Quod Erat Demonstrandum)

 

[Makematics]

hey guys, new question from cambridge :/ can't seem to do it lols

 

[Sy123]

hey guys, new question from cambridge :/ can't seem to do it lols

Don't think of y is as a variable. Consider the function:

 

[Makematics]

Don't think of y is as a variable. Consider the function:

wot why isnt y a variable? :S:S:S what makes x a variable and y a constant?

btw thanks for the swift reply

 

[asianese]

It doesn't matter in this question - if you differentiate wrt y you get the same answer.

 

[Sy123]

wot why isnt y a variable? :S:S:S what makes x a variable and y a constant?

btw thanks for the swift reply

This probably goes too deep into the definition of a constant and a variable and isn't really something I can explain (maybe someone else could shed some light on this).
From what I can tell with my limited knowledge:

When we differentiate, f(x) = ax + b, and we get f'(x) = a, why can't we consider a, a variable? I am quite certain if 'y' was replaced with 'A', you would get it right? Why can't we replace it then? after all it says nothing about an x-y plane.

I hope that made it a little clearer

 

[Makematics]

This probably goes too deep into the definition of a constant and a variable and isn't really something I can explain (maybe someone else could shed some light on this).
From what I can tell with my limited knowledge:

When we differentiate, f(x) = ax + b, and we get f'(x) = a, why can't we consider a, a variable? I am quite certain if 'y' was replaced with 'A', you would get it right? Why can't we replace it then? after all it says nothing about an x-y plane.

I hope that made it a little clearer

Actually that makes perfect sense, thanks so much! I think i get it now i just assumed that it was an x-y plane at first :/

 

[asianese]

note that conics that are not centred at the origin are not in the syllabus.

 

[braintic]

note that conics that are not centred at the origin are not in the syllabus.

But simple shifting of functions/relations is. They could easily justify slipping in such a question.

 

[Makematics]

 

[Sy123]

Try letting

 

[Makematics]

Try letting

tried that before i posted narrowed it down to cos (3theta)=sin(4theta), which i solved using general solutions... and it didnt work out very well

 

[HeroicPandas]

tried that before i posted narrowed it down to cos (3theta)=sin(4theta), which i solved using general solutions... and it didnt work out very well

did u use complementary angles to solve?

so have sinA = sinB, or cosA = cosB