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Question

# Parametric equation of (x−h)2 + (y−k)2 = r2 are x + h = rcosθ and y + k = rsinθ

A

True

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B

False

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Solution

## The correct option is B False Parametric equation, when substituted back in the equation, we get an identity. Lets try substituting the given parametric equation in the given equation. ⇒ x = −h + r cosθ and y = −k + r sinθ ⇒ (−h + r cosθ − h)2 + (−k + r cosθ − k)2 = r2 we can see that L.H.S is definitely not equal to r2. So the given parametric equation is wrong. In the figure 1, we have to express x and y in terms of r and θ. x−h is the length of base =r cosθ In the figure 1, we have to express x and y in terms of r and θ. x−h is the length of base =r cosθ ⇒ x − h = r cosθ or x = h + r cosθ Similarly y=k + r sinθ ⇒ x = h + r cosθ and y = k + r sinθ

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