TMUA Practice Question — Worked Solution

P1·Differentiation·5.5Mock 0 · P1 · Q11

tangentperpendicularparabolaroots of a quadraticparameter

A straight line with gradient

m

passes through the point

(1, k)

and meets the curve

y = 2 x^{2} - 4 x + 5

at two points

P

and

Q

.For which value of

k

are the tangents to the curve at

P

and

Q

perpendicular for every value of

m

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