Wrap Up Conics

Presentation

•

Mathematics

•

11th Grade

•

Practice Problem

•

Medium

•

CCSS

HSG.GPE.A.1, 7.G.A.3, HSG.GPE.A.3

Standards-aligned

Mike Pioquinto

Used 12+ times

FREE Resource

18 Slides • 30 Questions

Wrap Up Conics

UNIT 1

A conic section (or simply conic) is a curve obtained as the intersection of
the surface of a cone with a plane; the three types are parabolas, ellipses,
and hyperbolas. The general equation of a conic section is ax2 + Bx + Cy2 + Dy +
E = 0.

From the General Equation form, we can classify conics using the coefficient of x2

and y2.

If A=C, the equation yields to a circle.

If AC = 0, it is a parabola

If AC>O, it is an Ellipse

If AC<0, it is a Hyperbola

From the general equation of conics, we can write the equation to standard form by completing the square. The center of circle, ellipse and hyperbola and vertex of a parabola can be located at the origin or it can be shifted by h units horizontally and k units vertically.

Are you ready for the Wrap up Assessment?

Multiple Choice

Identify the conic:
-6x² + 4y² + 9x + y = -7

Circle

Parabola

Ellipse

Hyperbola

Multiple Choice

Find the directrix of the parabola:
(x - 4)² = 8(y + 3)

y = - 3

x= 5

y= - 5

y= 2

Multiple Choice

True or False?
When the x-part is squared, the parabola opens up or down.

True

False

Multiple Choice

Which direction does this parabola open?

Down

Left

Right

Multiple Choice

The focus is at (2,0) and the vertex is at (-4,0). What is the equation of the parabola?

y² = 24(x+4)

(y+4)² = -12x

x² = 16(y+4)

(x+4)² = -20y

Multiple Choice

A plane intersects a single nappe of a double-napped cone, such that it is perpendicular to the vertical axis of the cone. Which conic section is formed?

Multiple Choice

If a plane intersects a double-napped cone perpendicular to the base of the cone, but not through the vertex, what type of conic section is formed?

Circle

Ellipse

Hyperbola

Parabola

Multiple Choice

Which of the following is the graph of $\frac{\left(x+3\right)^2}{4}+\frac{\left(y+1\right)^2}{9}=1$

Multiple Choice

Find the standard equation of the given ellipse

Multiple Choice

Find the equation of circle whose is centre at ( -2, 3 ) and passing through the point ( -5, 4 )

$\left(x-2\right)^2+\left(y+3\right)^2=10$

$\left(x+2\right)^2+\left(y-3\right)^2=10$

$\left(x+4\right)^2+\left(y-3\right)^2=5$

$\left(x-4\right)^2-\left(y+3\right)^2=5$

Multiple Choice

Determine the centre and foci of an ellipse

$4x^2+y^2-16x-10y+25=0$

Centre (-2,3) and radius = $\left(5,\ 3\pm\sqrt{2}\right)$

Centre (4,-6) and radius = $\left(2,\ 3\pm\sqrt{4}\right)$

Centre (2, 5) and foci = $\left(2,\ 5\pm\sqrt{12}\right)$

Centre (3,-2) and foci= $\left(5,\ 2\pm\sqrt{12}\right)$

Multiple Choice

Identify the conic

$\frac{\left(x-2\right)^2}{4}+\frac{\left(y-5\right)^2}{16}=1$

Circle

Vertical Ellipse

Horizontal Hyperbola

Horizontal Ellipse

Multiple Choice

Identify the conic

$6y^2-5x-2y+5=0$

Parabola

Circle

Hyperbola

Ellipse

Multiple Choice

What are the major vertices of the ellipse?

(0, 0)

(7, 1) and (-1, 1)

(3, -5) and (3, 7)

(3, 5) and (4, 7)

Multiple Choice

Which equation shows an ellipse?

y^2+x-3y-15=0

$4x^2+4y^2-16y+81=0$

$2x^2-4y^2+18x+120y-159=0$

$16x^2+11y^2+54x-61y-121=0$

Multiple Choice

There are figures that formed by intersecting two inverted cones and a plane.

Cross Sections

Circles

Conic Sections

Parabolas

Multiple Choice

What is the vertex of the parabola: y=2(x-3)²+4

(3,4)

(-3,4)

(3, -4)

(-3,-4)

Multiple Choice

Classify the conic section.

Circle

Ellipse

Line

None of these

Multiple Choice

What kind of this formulae?

Circle

Parabola

Ellipse

Hyperbola

Multiple Choice

Which of the following is the type of conic sections as the surface of two cones with plane as figure?

Circle

Ellipse

Parabola

Hyperbola

Multiple Choice

Which equation shows an ellipse?

$y^2+x-3y-15=0$

$2x^2-4y^2+18x+120y-159=0$

$4x^2+4y^2-16y+81=0$

$16x^2+11y^2+54x-61y-121=0$

Multiple Select

Conics are special curves and are classified into four types. What are those?

Ellipse

Cone

Parabola

Hyperbola

Circle

Multiple Choice

When the cutting plane intersects the two cones parallel to their vertical axes and perpendicular to their bases, then the conic section is a _______________.

Parabola

Circle

Hyperbola

Ellipse

Multiple Choice

What type of conic section is $2x^2+2y^2-4x-16y-9=0$ ?

Circle

Parabola

Ellipse

Hyperbola

Multiple Select

Check the box that shows a parabola.

Multiple Choice

Identify the conic: 2x² + 6y – 9 = 0

Parabola Opens Up

Parabola Opens Down

Vertical Ellipse

Horizontal Ellipse

Multiple Choice

36x² – 5y² + 8x + 2y + 12 = 0

Hyperbola

Parabola

Ellipse

Circle

Multiple Choice

Which type of conic section is this equation?

circle

ellipse

hyperbola

parabola

Multiple Choice

Which type of conic section is this equation?

circle

ellipse

hyperbola

parabola

Multiple Choice

Which type of conic section is this equation?

circle

ellipse

hyperbola

parabola

Wrap Up Conics

UNIT 1

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