Mathematics A H230: Coordinate Geometry in the x-y Plane Topical Past Paper Questions

The points $A$ and $B$ have coordinates $(4, 8)$ and $(6, p)$ respectively, where $p$ is a positive constant and $p \neq 8$. (a) Find, in terms of $p$, the coordinates of the midpoint of $AB$. [1] (b) Find, in terms of $p$, the gradient of the line $AB$. The perpendicular bisecto…

The diagram shows the curve C with equation $ y = 4x^{2} - 10x + 7 $ and two straight lines, $ l_{1} $ and $ l_{2} $. The line $ l_{1} $ is the normal to C at the point $ \left(\frac{1}{2}, 3\right) $. The line $ l_{2} $ is the normal to C at the minimum point of C. (a) Determine…

The diagram shows the circle with equation $ x^{2}+y^{2}-6x+9y+19=0 $ and centre C. (a) Find the following. • The coordinates of $C$. • The exact radius of the circle. [3] The tangent to the circle at $D$ meets the $x$-axis at the point $A\left(\frac{55}{4},0\right)$ and the $y$-…