Step: 1

[Equation of conic.]

Step: 2

[Replace y = 0 to find the x - intercept.]

Step: 3

[Simplify.]

Step: 4

[Solve for x .]

Step: 5

So, the x - intercepts of the graph are (- 9, 0) and (9 , 0).

Step: 6

(0)^{2} + y ^{2} = 81

[Replace x = 0 to find the y - intercept.]

Step: 7

[Solve for y .]

Step: 8

So, the y - intercepts of the graph are (0, - 9) and (0, 9).

Step: 9

The equation x ^{2} + y ^{2} = 81 models a circle, since the intercepts are equidistant from the center, whcih is the origin.

Correct Answer is : a circle

Step: 1

9x ^{2} + 16y ^{2} = 144

[Equation of conic.]

Step: 2

9x ^{2} + 16(0)^{2} = 144

[Replace y = 0 to find the x - intercept.]

Step: 3

[Simplify.]

Step: 4

[Solve for x .]

Step: 5

So, the x - intercepts of the graph are (- 4, 0) and (4, 0).

Step: 6

9(0)^{2} + 16y ^{2} = 144

[Replace x = 0 to find the y - intercept.]

Step: 7

[Simplify.]

Step: 8

[Solve for y .]

Step: 9

So, the y - intercepts of the graph are (0, - 3) and (0, 3).

Step: 10

The equation 9x ^{2} + 16y ^{2} = 144 models an ellipse, since the intercepts are not equidistant from the center, which is the origin.

Correct Answer is : an ellipse

Step: 1

[Equation of conic.]

Step: 2

[Replace y = 0 to find the x - intercept.]

Step: 3

[Simplify.]

Step: 4

[Solve for x .]

Step: 5

So, the x - intercepts of the graph are (- 12, 0) and (12, 0).

Step: 6

(0)^{2} - y ^{2} = 144

[Replace x = 0 to find the y - intercept.]

Step: 7

[Simplify.]

Step: 8

The y - intercepts of the graph does not exist, since the equation y ^{2} + 144 = 0 has no real solutions.

[Discriminant of the quadratic equation is negative.]

Step: 9

The given conic section models a hyperbola, since it has one pair of intercepts (- 12, 0) and (12, 0).

Correct Answer is : a hyperbola

Step: 1

The plane is perpendicular to the axis of the cone. So, the resultant cross section will be a circle.

Correct Answer is : A circle

Step: 1

The path of the ball is a parabola.

Step: 2

The height of the ball begins at the lowest point.

Step: 3

The ball gets higher and slower, then eventually stops at the peak. Then the ball slowly descends and picks up speed until it hits the ground.

Step: 4

Since it has one peak where the ball stops and the slope is zero, it has to be a parabola.

Correct Answer is : parabola

Step: 1

Step: 2

[Seperate the y terms.]

Step: 3

[Complete the square.]

Step: 4

(y - 3)^{2} = 4(x - 3)

Step: 5

This equation is in the standard form (y - k )^{2} = 4p (x - h ), where h = 3, k = 3, and p = 4 4 = 1, which represents a parabola.

Correct Answer is : parabola

Step: 1

The correct statement is, 'A Conic section is the intersection of a plane and a cone'

Correct Answer is : A Conic section is the intersection of a plane and a cone.

Step: 1

The intersection of a right circular cone with a plane parallel to an element of the cone generates a plane curve known as a parabola.

Correct Answer is : a parabola

Step: 1

If no line of the cone is parallel to the plane, the intersection is a closed curve, known as an ellipse.

Correct Answer is : an ellipse

Step: 1

A plane curve having two branches, formed by the intersection of a plane with both halves of a right circular cone at an angle parallel to the axis of the cone known as a hyperbola.

Correct Answer is : a hyperbola

- Identifying and Using the Slopes of Parallel and Perpendicular Lines-Geometry-Solved Examples
- Writing Linear Equations of Parallel and Perpendicular Lines-Geometry-Solved Examples
- Equations of Circles-Geometry-Solved Examples
- Standard Forms and Equations of Ellipses and Parabolas-Geometry-Solved Examples
- Graphing Conic Sections-Geometry-Solved Examples

- Conic Section