Question

Find the length of the chord made by 3x2 - y2 = 3 and y + x – 5 = 0.

Answer 1

Answer:

The correct answer is "9√2 units".

Step-by-step explanation:

The given equations are:

⇒ $3x^2-y^2=3$...(equation 1)

⇒ $y+x-5=0$...(equation 2)

According to the 2nd equation, we get

⇒ $y+x-5=0$

⇒              $y=5-x$

On substituting the value of "y" in the 1st equation, we get

⇒  $3x^2-y^2=3$

     $3x^2-(5-x)^2=3$

     $3x^2-(25+x^2-10x)=3$

     $2x^2+10x-28=0$

On taking common, we get

     $x^2+5x-14=0$

On applying factorization, we get

     $x^2+7x-2x-14=0$

   $x(x+7)-2(x+7)=0$

           $(x+7)(x-2)=0$

                        $x+7=0$

                              $x=-7$

or,

                         $x-2=0$

                                $x=2$

Now,

The points are:

(-7, 12) = (x₁, y₁)

(2, 3) = (x₂, y₂)

By using the distance formula, the length of chord will be:

= $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

On substituting the values in the above formula, we get

= $\sqrt{(2-(-7))^2+(3-12)^2}$

= $\sqrt{(9)^2+(-9)^2}$

= $\sqrt{81+81}$

= $9 \sqrt{2}$ units