Weird Conics question (1 Viewer)

[Supra]

Hi guys can yall help with this...
Its 1993 HSC Question 3 part b i) and i have no idea

the circle has an equation of x²+y²+2gx+2fy+c=0 and pts R(x₀,y₀) P(x₁,y₁)
and Q(x₂,y₂) lie on the aforementioned circle

i)"If d is the distance between teh points R and P, show that

-d²/2= x₀x₁+y₀y₁+g(x₀+x₁)+f(y₀+y₁)+c

 

[CrashOveride]

Umm
distance formula. it comes out.
remember the points lie on the circle so they satisfy its equation.

 

[Supra]

ahh i get it tahts really easy, it looks difficult, and i did think of the distance formula, but i 4got the all important fact that u cud screw around with equations where u sub in R and P into the circle equation...thanks crash

 

[mojako]

Umm
distance formula. it comes out.
remember the points lie on the circle so they satisfy its equation.

explain to me pls..
my brain is.. severely damaged

 

[CrashOveride]

Well use the distance formula for RP. Also put the points R and P into the circle equation and isolate the x0 and y0 parts and the x1,y1 etc. Then chuck them back into the distance equation and after simplyifying etc. it should come out easily.

 

[CrashOveride]

when u sub x0 and y0 into that, then make them the subject of the equation or "isolate" them. Do the same with other point then chuck them back into distnace expression.