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What conic section does this equation represent?
STANDARD FORMS OF EQUATIONS OF CONIC SECTIONS:
| Circle | (x−h)2+(y−k)2=r2 |
|---|---|
| Ellipse with vertical major axis | (x−h)2b2+(y−k)2a2=1 |
| Hyperbola with horizontal transverse axis | (x−h)2a2−(y−k)2b2=1 |
| Hyperbola with vertical transverse axis | (y−k)2a2−(x−h)2b2=1 |
| Parabola with horizontal axis | (y−k)2=4p(x−h) , p≠0 |
How do you find the conic section of an equation?
How to Identify the Four Conic Sections in Equation Form
- Circle: When x and y are both squared and the coefficients on them are the same — including the sign.
- Parabola: When either x or y is squared — not both.
- Ellipse: When x and y are both squared and the coefficients are positive but different.
What if a hyperbola equation equals 0?
A circle (or ellipse) with the right hand side being negative. A hyperbola with the right hand side equal to zero. One variable is squared and the other variable is missing. If the right hand side is zero, then it is a line (x2 = 0 so x = 0) and if the right hand side is negative (x2 = -1), then there is no graph.
What is meant by Latus Rectum?
Definition of latus rectum : a chord of a conic section (such as an ellipse) that passes through a focus and is parallel to the directrix.
Which conic section does this equation represent 2x 2 9x 4y 2 8x 16?
Algebra Examples Since both variables are squared and the coefficients have the same sign but different coefficients, the conic is an ellipse.
How is a conic section formed?
Conic sections are generated by the intersection of a plane with a cone. If the plane is parallel to the axis of revolution (the y -axis), then the conic section is a hyperbola. Each conic is determined by the angle the plane makes with the axis of the cone.
Which equation represents the hyperbola?
Equations of Hyperbolas (continued) Quiz Flashcards | Quizlet.
What is ellipse equation?
What is the Equation of Ellipse? The equation of the ellipse is x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 . Here a is called the semi-major axis and b is the semi-minor axis. For this equation, the origin is the center of the ellipse and the x-axis is the transverse axis, and the y-axis is the conjugate axis.