Wrap Up Conics

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?

• Up
• 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