The coordinates of the focus of the parabola | vedclass

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(A) Given parametric equations are $x=5t^2+2$ and $y=10t+4$.From the second equation,$t = \frac{y-4}{10}$.Substituting $t$ into the first equation:$x-

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$(7,4)$

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(A) Given parametric equations are $x=5t^2+2$ and $y=10t+4$.From the second equation,$t = \frac{y-4}{10}$.Substituting $t$ into the first equation:$x-2 = 5\left(\frac{y-4}{10}\right)^2 = 5\left(\frac{(y-4)^2}{100}\right) = \frac{(y-4)^2}{20}$.Thus,$(y-4)^2 = 20(x-2)$.Comparing this with the standard form $(y-k)^2 = 4a(x-h)$,we have $h=2, k=4$,and $4a=20$,which gives $a=5$.The focus of the parabola $(y-k)^2 = 4a(x-h)$ is given by $(h+a, k)$.Substituting the values,the focus is $(2+5, 4) = (7,4)$.

The coordinates of the focus of the parabola described parametrically by $x=5t^2+2, y=10t+4$ (where $t$ is a parameter) are

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