$A B$ is a chord of the parabola $y^{2} = 4 a x$ with vertex $A$ . $B C$ is drawn perpendicular to $A B$ meeting the axis at $C$ . the projection of $B C$ on the axis of the parabola is

a

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2 a

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4 a

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8 a

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Solution

The correct option is C $4 a$
In $△ A B D$ , we have $tan θ = \frac{y}{x}$ ...(1)
In $△ B C D$ , we have $tan (90 - θ) = \frac{y}{C D}$
$\Rightarrow C D = y tan θ = \frac{y^{2}}{x}$ (Using (1))
$\Rightarrow C D = \frac{4 a x}{x} = 4 a$ $[∵ y^{2} = 4 a x]$

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AB is a chord of the parabola $y^{2} = 4 a x$ with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-

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AB is a chord of the parabola y2=4ax with vertex A. BC is drawn perpendicular to AB meeting the axis at C. the projection of BC on the axis of the parabola is

The correct option is C 4aIn △ABD, we have tanθ=yx ...(1) In △BCD, we have tan(90−θ)=yCD⇒CD=ytanθ=y2x (Using (1))⇒CD=4axx=4a [∵y2=4ax]

$A B$ is a chord of the parabola $y^{2} = 4 a x$ with vertex $A$ . $B C$ is drawn perpendicular to $A B$ meeting the axis at $C$ . the projection of $B C$ on the axis of the parabola is

The correct option is C $4 a$
In $△ A B D$ , we have $tan θ = \frac{y}{x}$ ...(1)
In $△ B C D$ , we have $tan (90 - θ) = \frac{y}{C D}$
$\Rightarrow C D = y tan θ = \frac{y^{2}}{x}$ (Using (1))
$\Rightarrow C D = \frac{4 a x}{x} = 4 a$ $[∵ y^{2} = 4 a x]$