Question

: Which conic section does the equation below describe?

(x+1)^2 + (y-3)^2 = 4

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


: Which conic section does the equation below describe?

(y-2)^2 = 12(x+7)

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

Answer 1

Answer on Question #57348 – Math – Analytic Geometry

Question

1) Which conic section does the equation below describe?

$$(x + 1)^2 + (y - 3)^2 = 4$$

A: Parabola

B: Ellipse

C: Circle

D: Hyperbola

Solution

Canonical equation for circle is $(x - x_0)^2 + (y - y_0)^2 = R^2$, hence equation $(x + 1)^2 + (y - 3)^2 = 4$ describes a circle.

Answer: C Circle.

Question

2) Which conic section does the equation below describe?

$$(y - 2)^2 = 12(x + 7)$$

A: Ellipse

B: Hyperbola

C: Circle

D: Parabola

Solution

Canonical equation for parabola is $y'^2 = 2px'$, where $y' = y - 2, x' = x + 7$, hence $(y - 2)^2 = 12(x + 7)$ describes a parabola.

Answer: D Parabola.

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