The equation of the circle drawn with the focus of the parabola $(x - 1)^{2} - 8 y = 0$ as its centre and touching the parabola at its vertex is

x^{2} + y^{2} - 4 y = 0

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x^{2} + y^{2} - 4 y + 1 = 0

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x^{2} + y^{2} - 2 x - 4 y = 0

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x^{2} + y^{2} - 2 x - 4 y + 1 = 0

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Solution

The correct option is D $x^{2} + y^{2} - 2 x - 4 y + 1 = 0$

$(x - 1)^{2} = 8 y$
REF.Image
$a = 2$
focus = $(1, 2)$ center of circle
Radius of circle = $2$
$\Rightarrow$ Eq $^{n}$ $\Rightarrow (x - 1)^{2} + (y - 2)^{2} = 4$
$\Rightarrow x^{2} - 2 x + y^{2} - 4 y + 1 = 0$ Ans
D is correct option.

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The equation of the circle drawn with the focus of the parabola (x−1)2−8y=0 as its centre and touching the parabola at its vertex is

The correct option is D x2+y2−2x−4y+1=0(x−1)2=8yREF.Imagea=2focus = (1,2) center of circleRadius of circle = 2⇒ Eqn ⇒(x−1)2+(y−2)2=4⇒x2−2x+y2−4y+1=0 Ans D is correct option.

The equation of the circle drawn with the focus of the parabola $(x - 1)^{2} - 8 y = 0$ as its centre and touching the parabola at its vertex is

The correct option is D $x^{2} + y^{2} - 2 x - 4 y + 1 = 0$

$(x - 1)^{2} = 8 y$
REF.Image
$a = 2$
focus = $(1, 2)$ center of circle
Radius of circle = $2$
$\Rightarrow$ Eq $^{n}$ $\Rightarrow (x - 1)^{2} + (y - 2)^{2} = 4$
$\Rightarrow x^{2} - 2 x + y^{2} - 4 y + 1 = 0$ Ans
D is correct option.