Equations of Conic Sections Systems of Non-linear Equations Solve eeach problem systematically 1. Find all values of m so that the graph 2mx2 − 16mx + my2 + 7y2=2m2 − 18m is a circle.

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Equations of Conic Sections  Systems of Non-linear Equations Solve eeach problem systematically 1. Find all values of m so that the graph 2mx2 − 16mx + my2 + 7y2=2m2 − 18m is a circle.

Gennenzip · Accepted Answer

Given equation is, 2mx2 − 16mx + my2 + 7y2=2m2 − 18m Which can be written as, x2 − 8x + m + 72ny2=m − 9  ⇒ x2 − 8x + 16 + m + 72m(y − 0)2=m − 9 + 16  ⇒(x − 4)2 + m + 72m(y − 0)2=m + 7 Equation of circle is given as, (x − a)2 + (y − b)2=r2 If the given equation is an equation of circle, then m + 72m should be equal to1 and m + 7 &amp;gt; 0 So,  m + 72m=1  m + 7=2m  m=7 And, m + 7=14 &amp;gt; 0, Therefore the graph 2 mx2 − 16 mx + my2 + 7y2=2m2 − 18m will be a circle if m=7

Equations of Conic Sections Systems of Non-linear Equations Solve eeach problem systematically 1. Find all values of m so that the graph 2mx^{2} - 16mx + my^{2} + 7y^{2} = 2m^{2} - 18m is a circle.

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