Show that the line y = x - 7 does not meet the circle (x + 2)^2 + y^2 = 33.
To find potential points of intersection between the line and the circle, we need to solve the equations simultaneously. So, we substitute y = x - 7 into the equation of the circle: (x + 2)2 + y2 = 33 (x + 2)2 + (x - 7)2 = 33 x2 + 4x + 4 + x2 - 14x + 49 = 33 (expand the brackets) 2x2 - 10x + 20 = 0 (collect like terms) x2 - 5x + 10 = 0 (divide each term by 2) Now, the discriminant b2 - 4ac = (-5)2 - 4 * 1 *10 = 25 - 40 = -15. As b2 - 4ac < 0, there is no solution to the quadratic equation. So, the line does not meet the circle.
AI
Related Maths A Level answers
All answers ▸It is given f(x)=(19x-2)/((5-x)(1+6x)) can be expressed A/(5-x)+B/(1+6x) where A and B are integers. i) Find A and B ii) Show the integral of this from 0 to 4 = Kln5
I struggle with modelling with differential equation, is there an easier way of interpreting this type of wordy question?
A cubic curve has equation y x3 3x2 1. (i) Use calculus to find the coordinates of the turning points on this curve. Determine the nature of these turning points.
Find, in radians, the general solution of the equation cos(3x) = 0.5giving your answer in terms of pi