Question

If x = h + a cos θ, y = k + b sin θ. 
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.

Answer 1

If is given that
x = h + a cos θ
and y = k + b sin θ

x - h = a cos θ           ....(i)
y - k = b sin θ           ....(ii)
The given equation is

`((x - h)/a)^2 + ((y - k)/(b))^2 = 1`

LHS = `((a cos θ)/a)^2 + ((b sin θ)/b)^2 `     ....(Putting the values of (i) and (ii)]

= cos²θ + sin²θ 
= 1 
= RHS
Hence proved.