If the focus of a parabola is (1, 0) and its | vedclass

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(C) The axis of the parabola is perpendicular to the directrix $x + y = 5$. Thus,the equation of the axis is of the form $x - y = k$.Since the axis pa

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$(2, 1)$

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(C) The axis of the parabola is perpendicular to the directrix $x + y = 5$. Thus,the equation of the axis is of the form $x - y = k$.Since the axis passes through the focus $(1, 0)$,we have $1 - 0 = k$,so $k = 1$. The equation of the axis is $x - y = 1$.The intersection of the axis $x - y = 1$ and the directrix $x + y = 5$ gives the point $Z$. Adding the two equations: $2x = 6 \implies x = 3$. Substituting $x=3$ into $x - y = 1$,we get $y = 2$. So,$Z = (3, 2)$.The vertex $V$ is the midpoint of the focus $S(1, 0)$ and the point $Z(3, 2)$.$V = \left( \frac{1 + 3}{2}, \frac{0 + 2}{2} \right) = (2, 1)$.

If the focus of a parabola is $(1, 0)$ and its directrix is $x + y = 5$,what is its vertex?

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