Find coordinate of focus, vertex and equation of directrix and the axis of the parabola $y = x^2 - 2x + 3$.

$y=x^2-2x+3 \Rightarrow x^2-2x = y-3 \Rightarrow (x-1)^2 = y-3+1=y-2$. So $(x-1)^2=(y-2)$. Let $X=x-1,\,Y=y-2$, so $X^2=4bY$ with $4b=1\Rightarrow b=\dfrac14$. - Vertex: $X=0,Y=0 \Rightarrow (1,2)$ - Focus: $X=0,\,Y=b \Rightarrow x=1,\,y=2+\dfrac14=\dfrac94 \Rightarrow \left(1,\dfrac94\right)$ …

Find coordinate of focus, vertex and equation of d – Class 11 Mathematics

Exercise 7.1 · Q20

y = x^2 - 2x + 3

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$y=x^2-2x+3 \Rightarrow x^2-2x = y-3 \Rightarrow (x-1)^2 = y-3+1=y-2$ .

So $(x-1)^2=(y-2)$ . Let $X=x-1,\,Y=y-2$ , so $X^2=4bY$ with $4b=1\Rightarrow b=\dfrac14$ .

Vertex: $X=0,Y=0 \Rightarrow (1,2)$
Focus: $X=0,\,Y=b \Rightarrow x=1,\,y=2+\dfrac14=\dfrac94 \Rightarrow \left(1,\dfrac94\right)$ …

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Q.Find coordinate of focus, vertex and equation of directrix and the axis of the parabola $y = x^2 - 2x + 3$ .

Concept understanding — Standard Equation of a Parabola

Q.Find coordinate of focus, vertex and equation of directrix and the axis of the parabola y=x2−2x+3y = x^2 - 2x + 3y=x2−2x+3.

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Q.Find coordinate of focus, vertex and equation of directrix and the axis of the parabola $y = x^2 - 2x + 3$ .

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