For what values of a and b is the line

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Differentiating y w.r.t. x

This is the slope of tangent to the parabola at any point x.

At x = 4

Slope of the tangent is

Given that

4x + y = b

is a tangent to the parabola at x = 4

The equation of tangent can be rewritten as

y = -4x + b

Comparing the above equation with slope intercept form of a line

y = mx + b (where m is the slope of the line)

we get, slope of the tangent = -4

Therefore,

So, equation of parabola becomes

y =

(4, -8) is the point at which the tangent touches the parabola.

Substitute x = 4 and y = -8 in the equation of tangent to find b

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