Question

Parametric equation of $(x-h{)}^2+(y-k{)}^2=r^{2}arex+h=rcos\theta andy+k=rsin\theta$

• A. True
• B. False

Answer 1

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.

$\Rightarrow x=-h+rcos\theta andy=-k+rsin\theta$

$\Rightarrow (-h+rcos\theta -h{)}^2+(-k+rcos\theta -k{)}^2=r^2$

we can see that L.H.S is definitely not equal to $r^2$. So the
given parametric equation is wrong.
In the figure 1, we have to express x and y in terms of r and $\theta$. $x-h$ is the length of base $=rcos\theta$

In the figure 1, we have to express x and y in terms of r and $\theta$. $x-h$ is the length of base $=rcos\theta$

$\Rightarrow x-h=rcos\theta orx=h+rcos\theta$

Similarly $y=k+rsin\theta$

$\Rightarrow x=h+rcos\theta andy=k+rsin\theta$