Applications: The circle test questions

1

What is the distance between the points \((3,4)\) and \(( - 1, - 2)\)?

2

What is the distance between the points \(( - 1,6)\) and \((2, - 4)\)?

3

If the point \(( - 2,p)\) lies on the circle with equation \({x^2} + {y^2} = 36\) then what is \(p\) equal to?

4

Do the pair of circles touch, intersect or miss?

\({(x + 1)^2} + {(y + 4)^2} = 13\) and \({(x - 7)^2} + {(y - 13)^2} = 52\)

5

Do the pair of circles touch, intersect or miss?

\({(x - 1)^2} + {(y - 5)^2} = 13\) and \({(x - 7)^2} + {(y - 14)^2} = 52\)

6

Do the pair of circles touch, intersect or miss?

\({(x - 8)^2} + {(y - 14)^2} = 13\) and \({(x - 7)^2} + {(y - 13)^2} = 52\)

7

Do the pair of circles touch, intersect or miss?

\({(x - 5)^2} + {(y - 10)^2} = 13\) and \({(x - 7)^2} + {(y - 13)^2} = 52\)

8

In solving a line with a circle, after substitution the following quadratics are obtained. Decide whether the solution indicates that the line would intersect, touch or miss the circle, and select the correct option.

\[{x^2} - 5x + 6 = 0\]

9

In solving a line with a circle, after substitution the following quadratics are obtained. Decide whether the solution indicates that the line would intersect, touch or miss the circle, and select the correct option.

\[{x^2} - 6x + 9 = 0\]

10

In solving a line with a circle, after substitution the following quadratics are obtained. Decide whether the solution indicates that the line would intersect, touch or miss the circle, and select the correct option.

\[3{x^2} - 3x + 5 = 0\]

11

In solving a line with a circle, after substitution the following quadratics are obtained. Decide whether the solution indicates that the line would intersect, touch or miss the circle, and select the correct option.

\[3{x^2} + 13x + 4 = 0\]

12

If the point \(\left( {(p + 1),(p + 2)} \right)\) lies on the circle with equation \({x^2} + {y^2} = 41\), what is \(p\) equal to?

13

The circle with centre \((2,3)\) and radius \(6\) has what equation?

14

The circle with centre \(( - 2,5)\) and radius \(\sqrt {29}\) has what equation?

15

The circle with equation \({x^2} + {y^2} + 14x - 2y + 5 = 0\) has its centre at:

16

What is the radius of the circle with equation \({x^2} + {y^2} - 8x + 6y + 12 = 0\)?