Question

For the parabola y2 =4ax the length of chord passing through the vertex and inclined to x axis at angle @ is

Answer 1

Length of chord =  $\frac{4acos\theta}{sin^2\theta}$

Step-by-step explanation:

Given,Equation of parabola,$y^2 = 4ax$..........................(1)

Vertex = (0,0)

$m = tan\theta$

Hence equation of chord, $y = (tan\theta)x$

Put this value in equation(1)$(tan^2\theta)x^2 = 4ax$

⇒ $x = \frac{4a}{tan^2\theta}$

$y = \frac{4a}{tan\theta}$

Length of chord = $\sqrt{(\frac{4a}{tan2t})^2 + (\frac{4a}{tan\theta})^2}$                                      

                           =$\frac{4a}{tan^2\theta}\sqrt{1 + tan^2\theta}$

                           =$\frac{4acos^2\theta{sin^2\theta}\times\frac{1{cot\theta}$

                           = $\frac{4acos\theta}{sin^2\theta}$

Hence,Length of chord =  $\frac{4acos\theta}{sin^2\theta}$

Answer 2

$\theta = \frac{4a\cos\theta}{\sin^2\theta}$

Step-by-step explanation:

given parabola = y² = 4ax

let the length of the chord be L  where chord cut the parabola is

$x_1=L \cos\theta\\\\y_1=L\sin\theta$

equation of the parabola

$y^2= 4ax$

this point will satisfy the equation of the parabola

$(L\sin\theta)^2 = 4a (L\cos\theta)\\\\L = \frac{4a\cos\theta}{\sin^2\theta}$

hence , The value is $\theta = \frac{4a\cos\theta}{\sin^2\theta}$

#Learn more:

If the chord y=mx+c subtends a right angle at the vertex of the parabola y²=4ax, then the value of c is

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