R (x, y) P (a,b) Q (c,d) are points on x^2 + y^2 + 2gx + 2fy +k = 0
i) if d is the distance between points R and P, show that:
-d^2/2 = x.a + y.b + g(x+a) + f(y+b) + k
I am not sure how to begin this question. Any approach is possible. Thanks guys
R (x, y) P (a,b) Q (c,d) are points on x^2 + y^2 + 2gx + 2fy +k = 0
i) if d is the distance between points R and P, show that:
-d^2/2 = x.a + y.b + g(x+a) + f(y+b) + k
I am not sure how to begin this question. Any approach is possible. Thanks guys
Hello, Lukybear!
Your variables are confusing.
. . is a coordinate . . . and a distance ?
. . is a coordinate . . . and a variable ?
I must revise the problem.
are points on: .
If is the distance between points and , show that:
. .
Add the equations: .
And we have: .
. . Hence: . .[1]
The distance between and is given by: .
And we have: .
. . Hence: . .[2]
Substitute [1] into [2]: .
And we have: .
. . Therefore: .