Question

Identify the conic section represented by the equation: x2 + 2x + 2y2 – 12y + 11 = 0 2

Answer 1

Answer:

Equation of the Ellipse

 $\frac{(x+1)^{2} }{8} + \frac{(y-3)^{2} }{4} = 1$

Step-by-step explanation:

Step(i):-

Given that the equation

                 x² + 2 x + 2y² - 12 y +11 = 0

      ⇒       x² + 2 x + 1 - 1 + 2(y² - 6 y )+ 11 = 0

                 x² + 2 x + 1 - 1 + 2(y² - 2(3) y+9-9 )+ 11 = 0

     ⇒        x² + 2 x + 1 - 1 + 2(y² - 2(3 y ) +  3²- 3² ) + 11 = 0

By using (a +b)² = a² + 2 a b + b²

               (a -b)² = a² - 2 a b + b²

Step(ii):-

          x² + 2 x + 1 - 1 + 2(y² - 2(3 y ) +  3²- 3² ) + 11 = 0

    ⇒  ( x+1)² +2( y-3 )² - 1 - 2(9) +11 =0

   ⇒   ( x+1)² +2( y-3 )² - 8 =0

           ( x+1)² +2( y-3 )² = 8

Dividing '8' on both sides , we get

         $\frac{(x+1)^{2} }{8} + \frac{2(y-3)^{2} }{8} = 1$

      $\frac{(x+1)^{2} }{8} + \frac{(y-3)^{2} }{4} = 1$

This equation represents the Ellipse