Question

the length of chord of the parabola y2=8x having equation 3y-4x+8=0​

Answer 1

Given :

The equation of parabola is y² = 8 x

The equation of chord is 3 y - 4 x + 8 = 0

To Find :

The length of the chord

Solution :

∵  equation of chord   3 y - 4 x + 8 = 0

Or,       3 y = 4 x - 8

Or,          y = $\dfrac{4}{3}$ x - $\dfrac{8}{3}$

So, The slope chord = tanα = $\dfrac{4}{3}$

or,    y² = 8 x

Or.    y² = 4 × 2 x

i.e    a = 2

The point are ( 0 ,  0 ) and  ( 4 a tanα   , 4 a tan²α )

Or,   $x_1 , y _1$   = 0 , 0

And  $x_2 , y_2$  =  4 a tanα   , 4 a tan²α  

                            = 8 × $\dfrac{4}{3}$  , 8 × $\dfrac{16}{9}$  =  $\dfrac{32}{3}$ ,  $\dfrac{128}{3}$

Again

The length of chord = L = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }$

                                       = $\sqrt{(\dfrac{32}{3} -0)^{2}+(\dfrac{128}{3} -0)^{2} }$

                                      = $\sqrt{(10.67)^{2}+(72.67)^{2} }$

∴ The length of chord = L = 73.44  unit

Hence, The length of the chord is 73.44 unit   Answer