2024 MI P1 Q4
2024 MI P1 Q4
8 marks
The equation of a curve is \(2xy + (1 + y)^2 = x\).
- Find the equations of the two tangents which are parallel to the \(y\)-axis.[4]
- The normal to the curve at the point \(A(-4, 5)\) meets the curve again at the point \(B\). Find the coordinates of point \(B\).[4]
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Answer:(i) \(x=0\) and \(x=-3\) (ii) \(\displaystyle B\left(-\frac{1225}{88},\frac{13}{22}\right)\approx(-13.9,0.591)\) (3 s.f.)
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