Line intersecting general conic

A question is this type if and only if it asks to find intersection points of a line with a circle, ellipse, or other conic section (x² + y² or similar implicit form).

31 questions · Moderate -0.4

1.02c Simultaneous equations: two variables by elimination and substitution
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Edexcel C1 Q4
7 marks Moderate -0.5
Solve the simultaneous equations $$y = x - 2,$$ $$y^2 + x^2 = 10.$$ [7]
Edexcel C1 Q37
11 marks Standard +0.3
\includegraphics{figure_2} Figure 2 shows the curve with equation \(y^2 = 4(x - 2)\) and the line with equation \(2x - 3y = 12\). The curve crosses the \(x\)-axis at the point \(A\), and the line intersects the curve at the points \(P\) and \(Q\).
  1. Write down the coordinates of \(A\). [1]
  2. Find, using algebra, the coordinates of \(P\) and \(Q\). [6]
  3. Show that \(\angle PAQ\) is a right angle. [4]
Edexcel M2 2014 January Q3
7 marks Moderate -0.5
Solve the simultaneous equations $$x - 2y - 1 = 0$$ $$x^2 + 4y^2 - 10x + 9 = 0$$ [7]
Edexcel C1 Q5
11 marks Standard +0.3
\includegraphics{figure_1} Figure 1 shows the curve with equation \(y^2 = 4(x - 2)\) and the line with equation \(2x - 3y = 12\). The curve crosses the \(x\)-axis at the point \(A\), and the line intersects the curve at the points \(P\) and \(Q\).
  1. Write down the coordinates of \(A\). [1]
  2. Find, using algebra, the coordinates of \(P\) and \(Q\). [6]
  3. Show that \(\angle PAQ\) is a right angle. [4]
Edexcel C1 Q5
7 marks Moderate -0.3
Solve the simultaneous equations \begin{align} x + y &= 2
3x^2 - 2x + y^2 &= 2 \end{align} [7]
OCR H240/01 2017 Specimen Q1
4 marks Moderate -0.5
Solve the simultaneous equations. \(x^2 + 8x + y^2 = 84\) \(x - y = 10\) [4]