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Quadratic Functions (1 Viewer)

skillstriker

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Find the equation of the two lines which contain the point (1,3) and are tangents to the parabola y = x2​-2x+3
 

Carrotsticks

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Let the line be y=mx+b

Substitute into the equation of the parabola and put it in quadratic form yields:



Let the discriminant be equal to 0:



The line passes through (1,3) so we sub that into the equation y=mx+b:



Solve simultaneously with the quadratic we had:



Thus, there exist no real solutions for m.

Therefore, there are no tangents that can be drawn from M which pass through (1,3).

This is also clearly seen via a diagram if you sketch the curve and the point. You will see that the point lies 'inside' the parabola, so no tangents can be drawn.
 

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