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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`.
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Solution
Given: x = h + a cos θ
x − h = a cos θ ...(i)
y = k + b sin θ
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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