Question

: Which conic section does this equation represent?

X^2 - 4x + y^2 + 6y – 9 = 5

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

: Which conic section is represented by the equation shown below?
9x + 4y^2 + 18x = 16

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

Answer 1

Answer on Question #57344 – Math – Analytic Geometry

Question

1. Which conic section does this equation represent?

$$X ^ {\wedge} 2 - 4 x + y ^ {\wedge} 2 + 6 y - 9 = 5$$

A: Parabola

B: Hyperbola

C: Circle

D: Ellipse

Solution

$$x ^ {\wedge} 2 - 4 x + y ^ {\wedge} 2 + 6 y - 9 = 5$$ $$(x - 2) ^ {\wedge} 2 - 4 + (y + 3) ^ {\wedge} 2 - 9 - 9 = 5$$ $$(x - 2) ^ {\wedge} 2 + (y + 3) ^ {\wedge} 2 = 2 7$$

It is an equation of circle. Coordinates of centre are $(2, -3)$ and radius is $r = \sqrt{27} = 3\sqrt{3}$.

Answer: C: Circle

Question

2. Which conic section is represented by the equation shown below?

$$9 x + 4 y ^ {\wedge} 2 + 18 x = 16$$

A: Circle

B: Hyperbola

C: Parabola

D: Ellipse

Solution

$$9 x + 4 y ^ {\wedge} 2 + 18 x = 16$$ $$4 y ^ {\wedge} 2 = 16 - 27 x$$ $$y ^ {\wedge} 2 = 4 - 27/4 x$$ $$y ^ {\wedge} 2 = -27/4 (x - 16/27)$$

It is an equation of parabola. Coordinates of vertex are $(16/27, 0)$.

Answer: C: Parabola.

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