If a chord,which is not a tangent,of the para | vedclass

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Question

(D) The equation of the parabola is $y^2=16x$. The equation of the chord is $2x+y=p$. The equation of a chord with midpoint $(h, k)$ is given by $T=S_

Vedclass · Accepted Answer

$p=2, h=3, k=-4$

Vedclass · Answer

(D) The equation of the parabola is $y^2=16x$. The equation of the chord is $2x+y=p$. The equation of a chord with midpoint $(h, k)$ is given by $T=S_1$,where $T$ is the tangent form and $S_1$ is the value of the parabola equation at $(h, k)$. $yk-8(x+h) = k^2-16h$ $yk-8x = k^2-8h$ Comparing this with the given chord equation $y = -2x+p$ or $2x+y=p$: $\frac{k}{1} = \frac{-8}{2} = \frac{k^2-8h}{p}$ From $\frac{k}{1} = -4$,we get $k=-4$. From $\frac{-8}{2} = \frac{k^2-8h}{p}$,we get $-4 = \frac{(-4)^2-8h}{p} = \frac{16-8h}{p}$. $-4p = 16-8h$ $\Rightarrow 8h-4p = 16$ $\Rightarrow 2h-p = 4$. Checking the options: For option $D$: $p=2, h=3, k=-4$. $2(3)-2 = 6-2 = 4$. This satisfies the condition. Thus,the correct option is $D$.

If a chord,which is not a tangent,of the parabola $y^2=16x$ has the equation $2x+y=p$,and midpoint $(h, k)$,then which of the following is(are) possible value$(s)$ of $p, h$ and $k$?

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