The points of contact Q and R of the tangents | vedclass

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(B) For a parabola $y^2 = 4ax$,the chord of contact from a point $(x_1, y_1)$ is given by $yy_1 = 2a(x + x_1)$.Here,$a = 1$ and the point is $(2, 3)$,

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$(1, 2)$ and $(4, 4)$

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(B) For a parabola $y^2 = 4ax$,the chord of contact from a point $(x_1, y_1)$ is given by $yy_1 = 2a(x + x_1)$.Here,$a = 1$ and the point is $(2, 3)$,so the chord of contact is $3y = 2(x + 2)$,which simplifies to $3y = 2x + 4$,or $x = \frac{3y - 4}{2}$.Substituting this into the parabola equation $y^2 = 4x$:$y^2 = 4(\frac{3y - 4}{2})$$y^2 = 2(3y - 4)$$y^2 - 6y + 8 = 0$$(y - 2)(y - 4) = 0$Thus,$y = 2$ or $y = 4$.If $y = 2$,$x = \frac{3(2) - 4}{2} = \frac{2}{2} = 1$.If $y = 4$,$x = \frac{3(4) - 4}{2} = \frac{8}{2} = 4$.The points of contact are $(1, 2)$ and $(4, 4)$.

The points of contact $Q$ and $R$ of the tangents drawn from the point $P(2, 3)$ to the parabola $y^2 = 4x$ are

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