A variable straight line is represented by the equation
MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane
Problem
A variable straight line is represented by the equation px−6y+18=0, where p is a real parameter.
(i) Obtain expressions for the slope, the x-intercept, and the y-intercept of the line in terms of p.
(ii) The triangle bounded by the line and the coordinate axes is required to have a constant area of 18 square units. Derive the quadratic equation that p must satisfy.
(iii) Solve the quadratic equation obtained in part (ii) and hence write the two possible equations of the line that meet the given area condition.