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