A circle C C\,C has centre (10,6)(10, 6)(10,6) and radius 2172\sqrt{17}217. A line L L\,L has equation y=mxy = mxy=mx.
Show that the xxx-coordinate of any points of intersection of C C\,C and L L\,L satisfies the equation (m2+1)x2−(12m+20)x+68=0(m^2 + 1)x^2 - (12m + 20)x + 68 = 0(m2+1)x2−(12m+20)x+68=0.
Find values of m m\,m for which the equation in (a) has equal roots.
Two lines drawn from the origin which are tangents to CCC. Find the coordinates of the points of contact between the tangents and CCC.
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.