# 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 $${x^2} + {y^2} - 8x + 6y + 12 = 0$$?