E-LC02 · A family of secants and tangents
The circle is \((x+2)^2+(y-1)^2=16\). Consider the family of lines \(y=2x+k\).
By substituting the line equation, show that the intersection quadratic has discriminant \(320-4(k-5)^2\). You may use \(u=x+2\).
Find both tangent values of k. Give the full sets of k-values for two distinct intersections and for no real intersections.
Find the intersection coordinates when \(\displaystyle k=5\), and explain the chord geometry.
Complete-answer checking, worked solutions and indicative written criteria.
Open the complete answer form