Question

: Which conic section does the equation below describe?

(x+2)^2 (y-9)^2
---------- + ------------ = 1
16 36

A: Circle
B: Hyperbola
C: Parabola
D: Ellipse

: Which conic section does the equation below describe?

(x+2)^2 = 4(y-3)

A: Parabola
B: Circle
C: Ellipse
D: Hyperbola

Answer 1

Answer on Question #57349 – Math – Analytic Geometry

Question

1) Which conic section does the equation below describe?

$$\frac{(x + 2)^2}{16} + \frac{(y - 9)^2}{36} = 1$$

A: Parabola

B: Ellipse

C: Circle

D: Hyperbola

Solution

Equation $\frac{(x + 2)^2}{16} + \frac{(y - 9)^2}{36} = 1$ is transformed to a canonical equation for ellipse

$$\frac{x'^2}{a^2} + \frac{y'^2}{b^2} = 1, \text{ where } x' = x + 2, y' = y - 9.$$

Answer: B: Ellipse.

Question

2) Which conic section does the equation below describe?

$$(x + 2)^2 = 4(y - 3)$$

A: Ellipse

B: Hyperbola

C: Circle

D: Parabola

Solution

Equation $(x + 2)^2 = 4(y - 3)$ is transformed to a canonical equation for parabola $y'^2 = 2px'$, where $y' = x + 2, x' = y - 3$.

Answer: D: Parabola.

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