What is the equation of reflection of the curve y = 5 x 2 − 7 x + 2about the pont (3, -3)?

Question

What is the equation of reflection of the curve  y  =  5      x          2        −  7  x  +  2about the pont (3, -3)?

Tristan Ward · Accepted Answer

Step 1Let&#039;s use the following steps:shift the coordinate system so that the point of reflection becomes the originreflect around the origin.The reflection of a point (x, y) equals the point (-x, -y).shift our coordinate system back to its original position.Applying to your question:Let       y    ′    =  y  +  3 and       x    ′    =  x  −  3 . The point of reflection is the origin in our new coordinate system. Our original curve now has equation      y    ′    −  3  =  5  (      x    ′    +  3      )    2    −  7  (      x    ′    +  3  )  +  2.Reflect around the origin. Replace each       x    ′   by   −      x    ′   and each       y    ′   by   −      y    ′   . The reflected curve has equation  −      y    ′    −  3  =  5  (  −      x    ′    +  3      )    2    −  7  (  −      x    ′    +  3  )  +  2.Go back to the original coordinates. The curve we are looking for has equation  −  (  y  +  3  )  −  3  =  5  (  −  (  x  −  3  )  +  3      )    2    −  7  (  −  (  x  −  3  )  +  3  )  +  2.Now rewrite until you obtain an equation of the form   y  =  … .

Rachel Villa · Accepted Answer

Step 1I&#039;ll solve it without coordinate interchanging.This curve is parabola, and reflected curve is parabola, so trivially. And the vertex of this curve is   (      7    10    ,  −      9    20    ) , and focus of this curve is   (      7    10    ,  −      2    5    ) .So vertex of reflected curve is   (      53    10    ,  −      111    20    ) , and focus is   (      53    10    ,  −      28    5    ) .So, the equation of curve must be   y  =  −  5      x    2    +  53  x  −  146 .

What is the equation of reflection of the curve y = 5 x <mrow class="MJX-Te

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