Asked by Jonathan Catano on Jun 17, 2024
Verified
Identify the vertex and focus of the parabola y2=−7xy ^ { 2 } = - 7 xy2=−7x .
A) vertex: (0,0) focus: (−74,0) \left( - \frac { 7 } { 4 } , 0 \right) (−47,0)
B) vertex: (0,0) focus: (−17,0) \left( - \frac { 1 } { 7 } , 0 \right) (−71,0)
C) vertex: (0,0) focus: (-7,0)
D) vertex: (0,0) focus: (0,74) \left( 0 , \frac { 7 } { 4 } \right) (0,47)
E) vertex: (0,0) focus: (0,17) \left( 0 , \frac { 1 } { 7 } \right) (0,71)
Vertex
The highest or lowest point of a parabola where it changes direction, or a corner point of a geometric shape.
Focus
In geometry and optics, the point where rays or waves meet or from which they diverge, especially after reflection or refraction.
- Comprehend the canonical forms of parabola equations and their connection to the focus and vertex.
- Enhance the capability to pinpoint critical elements of conic sections like center, radius, vertices, co-vertices, and foci.
Verified Answer
RR
Randa RegesJun 21, 2024
Final Answer :
A
Explanation :
We can see that the given equation is of the form $y^2 = 4px$ with $p = -\frac{7}{4}$. Therefore, the vertex is at the origin $(0,0)$ and the focus is at $\left(-\frac{p}{2},0\right) = \left(-\frac{7}{4 \cdot 2},0\right) = \left(-\frac{7}{4},0\right)$. So, the correct choice is $\textbf{(A)}$.
Learning Objectives
- Comprehend the canonical forms of parabola equations and their connection to the focus and vertex.
- Enhance the capability to pinpoint critical elements of conic sections like center, radius, vertices, co-vertices, and foci.