Conic Sections & Equations Of The Circle

Question 1

The center of a circle is (0,10). The radius is 10.

Find k.

Answer 1

10

Question 2

Determine the center and the radius of the circle : (x-1)^2 + (y+2)^2 = 64

Answer 2

C (1,-2) ; r = 8

Question 3

Determine the center and the radius of the circle: x^2 + y^2 + 14x - 8y + 16 = 0

Answer 3

C (-7, 4); r = 7

Question 4

Determine the value of h in its center: x^2 + y^2 + 12x - 10y - 3 = 0

Answer 4

-6

Question 5

The center of a circle is (10,-6). The radius is 10. Find h.

Answer 5

10

Question 6

This is formed when a nappe is intersected by a plane that is parallel to the base of the cone.

Answer 6

Circle

Question 7

This is any one of the two cones joined through their vertices.

Answer 7

Nappe

Question 8

This is formed when a nappe is intersected by a plane that is unparallel to any generator of the cone.

Answer 8

Ellipse

Question 9

The center of a circle is (2,6). If the radius is 10 determine its equation in standard form.

Answer 9

(x-2)^2 + (y-6)^2 = 100

Question 10

This is formed when a nappe is intersected by a plane that is parallel to any generator of the cone.

Answer 10

Parabola

Question 11

Write the equation in standard form: x^2 + y^2 + 12x - 10y - 3 = 0

Answer 11

(x+6)^2 + (y-5)^2 = 64

Question 12

The equation of the circle centered at (-3,5) and whose radius is 8 units.
Find r.

Answer 12

8

Question 13

The Circle centered at (-3,5) and whose radius is 8 units. Find r^2.

Answer 13

64

Question 14

Determine the value of r as the radius of the given.

x^2 + y^2 - 10x + 12y - 3 = 0

Answer 14

8

Question 15

The equation of the circle centered at (-3,5) and whose radius is 8 units.
Find h.

Answer 15

-3

Question 16

The center of a circle is (0,-6). The radius is 10

Find r^2

Answer 16

100

Question 17

Determine the center and the radius of the circle x^2+y^2=81.
Center:
radius:

Answer 17

C (0,0); r = 9

Question 18

Find the equation of the circle centered at (-3,4) and whose radius is 6 units. (Standard Form)

Answer 18

(x+3)^2 + (y-4)^2 = 36

Question 19

The center of a circle is (0,-6). The radius is 6

Find r

Answer 19

6

Question 20

The circle centered at (-3,5) and whose radius is 8 units. Find k.

Answer 20

5

Question 21

This is formed when two nappes are intersected by a plane that is perpendicular to the bases of the cone.

Answer 21

Hyperbola

Question 22

The two lines from the opposite sides of a right cylinder that can be rotated through their midpoints to form two cones joining through their vertices.

Answer 22

Generators

Question 23

Determine the value of k in its center .

x^2 + y^2 + 12x - 10y - 3 = 0

Answer 23

5