Range of k, line not intersecting curve

A question is this type if and only if it asks for the set of values of a constant m or k for which a given line does not cross or touch a given curve, using the discriminant strictly less than zero condition.

4 questions · Moderate -0.1

1.02d Quadratic functions: graphs and discriminant conditions
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Edexcel P1 2020 January Q8
6 marks Moderate -0.3
8. The straight line \(l\) has equation \(y = k ( 2 x - 1 )\), where \(k\) is a constant. The curve \(C\) has equation \(y = x ^ { 2 } + 2 x + 11\) Find the set of values of \(k\) for which \(l\) does not cross or touch \(C\).
(6)
OCR MEI C1 2016 June Q11
12 marks Standard +0.3
11
  1. Find the coordinates of the points of intersection of the curve \(y = 2 x ^ { 2 } - 5 x - 3\) with the axes.
  2. Find the coordinates of the points of intersection of the curve \(y = 2 x ^ { 2 } - 5 x - 3\) and the line \(y = x + 3\).
  3. Find the set of values of \(k\) for which the line \(y = x + k\) does not intersect the curve \(y = 2 x ^ { 2 } - 5 x - 3\). \section*{END OF QUESTION PAPER}
CAIE P1 2016 November Q1
3 marks Moderate -0.3
Find the set of values of \(k\) for which the curve \(y = kx^2 - 3x\) and the line \(y = x - k\) do not meet. [3]
CAIE P1 2018 November Q10
9 marks Moderate -0.3
The equation of a curve is \(y = 2x + \frac{12}{x}\) and the equation of a line is \(y + x = k\), where \(k\) is a constant.
  1. Find the set of values of \(k\) for which the line does not meet the curve. [3]
In the case where \(k = 15\), the curve intersects the line at points \(A\) and \(B\).
  1. Find the coordinates of \(A\) and \(B\). [3]
  2. Find the equation of the perpendicular bisector of the line joining \(A\) and \(B\). [3]