Conic Sections Parabola Equation

The conics form of the equation has subtraction inside the parentheses so the x 3 2 is really x 3 2 and the vertex is at 3 1.

Conic sections parabola equation. Length of transverse axis. X a 2 y 2 x a 2. If p 0 the parabola opens upward and if p 0 the parabola opens downward.

Solving for p. R l 1 e cos θ displaystyle r frac l 1 e cos theta. P 3 4 the focus of the parabola which is in standard form y 2 4 p x is p 0.

Nothing else matters signs and coefficients change the physical appearance of the parabola which way it opens or how fat it is but don t change the fact that it s a parabola. State the vertex the directrix and any intercepts of the parabola having the equation x 3 2 20 y 1. In the first equation you see an x 2 but no y 2 and in the second equation you see a y 2 but no x 2.

Pf x a 2 y 2 also pb x a 2. Since pf pb from eq. Y k 2 4p x h where p 0.

Comparing with the given equation y2 4ax we find that a 4. X2 y2 r2. The equation is of the form y 2 4 p x where 4 p 3.

Learn vocabulary terms and more with flashcards games and other study tools. Also by the distance formula we know that. The equations y x 2 4 and x 2y 2 3y 10 are both parabolas.