Application of DerivativeHard

Question

Equation of the line through the point (1/2, 2) and tangent to the parabola y = + 2 and secant to the curve y = is -

Options

A.2x + 2y - 5 = 0
B.2x + 2y - 9 = 0
C.y - 2 = 0
D.none

Solution

    
Equation of tangent is y - 2 = m
y = mx + 2 -
Put it in the parabolas mx + 2 - + 2
+ mx - = 0
since D = 0       ⇒ m2 + m = 0
m = 0,-1
Two tangents are three (i) y = 2
(ii) y = - x + 2 +
⇒ y = - x +
The line y = 2 is tangent but ⇒ y = - x + is secant for the curve

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