What is the distance between the points \((3,4)\) and \(( - 1, - 2)\)?
\[\sqrt {20}\]
\[\sqrt {40}\]
\[\sqrt {52}\]
What is the distance between the points \(( - 1,6)\) and \((2, - 4)\)?
\[\sqrt {109}\]
\[\sqrt {89}\]
\[\sqrt {66}\]
If the point \(( - 2,p)\) lies on the circle with equation \({x^2} + {y^2} = 36\) then what is \(p\) equal to?
\[\pm \sqrt {40}\]
\[\pm \sqrt {32}\]
\[\pm \sqrt {38}\]
Do the pair of circles touch, intersect or miss?
\({(x + 1)^2} + {(y + 4)^2} = 13\) and \({(x - 7)^2} + {(y - 13)^2} = 52\)
The circles touch externally
The circles intersect
The circles miss
\({(x - 1)^2} + {(y - 5)^2} = 13\) and \({(x - 7)^2} + {(y - 14)^2} = 52\)
The circles touch internally
\({(x - 8)^2} + {(y - 14)^2} = 13\) and \({(x - 7)^2} + {(y - 13)^2} = 52\)
\({(x - 5)^2} + {(y - 10)^2} = 13\) and \({(x - 7)^2} + {(y - 13)^2} = 52\)
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.
\[{x^2} - 5x + 6 = 0\]
The lines intersect
The lines touch
The lines miss
\[{x^2} - 6x + 9 = 0\]
\[3{x^2} - 3x + 5 = 0\]
\[3{x^2} + 13x + 4 = 0\]
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?
\(3\) or \(- 6\)
\(4\) or \(5\)
\(- 4\) or \(- 5\)
The circle with centre \((2,3)\) and radius \(6\) has what equation?
\[{x^2} + {y^2} + 4x + 6y - 23 = 0\]
\[{x^2} + {y^2} - 4x - 6y - 23 = 0\]
\[{x^2} + {y^2} - 6x - 4y - 23 = 0\]
The circle with centre \(( - 2,5)\) and radius \(\sqrt {29}\) has what equation?
\[{x^2} + {y^2} - 4x + 10y = 0\]
\[{x^2} + {y^2} - 10x + 4y = 0\]
\[{x^2} + {y^2} + 4x - 10y = 0\]
The circle with equation \({x^2} + {y^2} + 14x - 2y + 5 = 0\) has its centre at:
\[(1, - 7)\]
\[(7, - 1)\]
\[( - 7,1)\]
What is the radius of the circle with equation \({x^2} + {y^2} - 8x + 6y + 12 = 0\)?
\[\sqrt {13}\]
\[\sqrt {37}\]
\[\sqrt {88}\]