Find the vertex,focus,and directrix of the parabola. $y ^ { 2 } = 10 x$
A)Vertex: (0,0);Focus: $\left( \frac { 10 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 10 } { 4 }$
B)Vertex: (0,0);Focus: $\left( \frac { 1 } { 10 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 10 }$
C)Vertex: (0,0);Focus: $\left( - \frac { 10 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 10 } { 4 }$
D)Vertex: (0,0);Focus: $\left( - \frac { 10 } { 4 } , 0 \right)$ ;Directrix: $x = \frac { 10 } { 4 }$
E)Vertex: (0,0);Focus: $\left( - \frac { 1 } { 10 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 10 }$

Question

Find the vertex,focus,and directrix of the parabola.​ $y ^ { 2 } = 10 x$ ​
A)Vertex: (0,0);Focus: $\left( \frac { 10 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 10 } { 4 }$
B)Vertex: (0,0);Focus: $\left( \frac { 1 } { 10 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 10 }$
C)Vertex: (0,0);Focus: $\left( - \frac { 10 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 10 } { 4 }$
D)Vertex: (0,0);Focus: $\left( - \frac { 10 } { 4 } , 0 \right)$ ;Directrix: $x = \frac { 10 } { 4 }$
E)Vertex: (0,0);Focus: $\left( - \frac { 1 } { 10 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 10 }$

Quizplus · Accepted Answer

The equation $y^2 = 10x$ represents a parabola opening to the right with its vertex at the origin (0,0). The general form of such a parabola is $y^2 = 4px$, where $p$ is the distance from the vertex to the focus and also from the vertex to the directrix. Here, $4p = 10$, so $p = \frac{10}{4}$. Therefore, the focus is $\left(\frac{10}{4}, 0\right)$ and the directrix is $x = -\frac{10}{4}$.

Find the Vertex,focus,and Directrix of the Parabola y2=10xy ^ { 2 } = 10 xy2=10x

Find the Vertex,focus,and Directrix of the Parabola $y ^ { 2 } = 10 x$