What is the angle in degrees between the tang | vedclass

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(A) Let the line passing through the origin be $y = mx$.If this line is a tangent to the parabola $y^2 = 4a(x - a)$,then substituting $y = mx$ into th

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$90$

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(A) Let the line passing through the origin be $y = mx$.If this line is a tangent to the parabola $y^2 = 4a(x - a)$,then substituting $y = mx$ into the equation gives:$(mx)^2 = 4a(x - a)$$m^2x^2 - 4ax + 4a^2 = 0$For the line to be a tangent,the discriminant of this quadratic equation must be zero:$D = (-4a)^2 - 4(m^2)(4a^2) = 0$$16a^2 - 16a^2m^2 = 0$$16a^2(1 - m^2) = 0$Since $a 
eq 0$,we have $m^2 = 1$,which implies $m = 1$ or $m = -1$.The slopes of the two tangents are $m_1 = 1$ and $m_2 = -1$.Since $m_1 	imes m_2 = 1 	imes (-1) = -1$,the tangents are perpendicular to each other.Therefore,the angle between them is $90^o$.

What is the angle in degrees between the tangents drawn from the origin to the parabola $y^2 = 4a(x - a)$?

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