Tangents to a parabola from an external point
Tangents to a parabola from an external point
IP 3
8 marks
The line \(y=mx+c\) and the curve \(y=x^2+1\) are drawn on the same axes, where \(m\) and \(c\) are constants.
- Show that the line is a tangent to the curve exactly when \(4c=4-m^2\).[3]
- Hence find the equations of the two tangents to the curve that pass through the point \((1,-2)\).[3]
- Explain why no tangent to the curve passes through the point \((0,2)\).[2]
Solution:
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Answer:(a) shown (b) \(y=6x-8\) and \(y=-2x\) (c) \(m^2=-4\) has no real solution; \((0,2)\) lies above the curve
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