The exercise provides the equation for a degenerate conical section. Fill in the square and describe the graph of each equation. 4x2−y2−32x−4y+60=0

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Usamah Prosser · Accepted Answer

Step 1  Completing the square:  Since the equation has x and y squared terms on the left and 0 on the right, the equation represents pair of lines crossing each other at (4,−2).  4x2−y2−32x−4y+60=0  4x2−32x−y2−4y=−60  4(x2−8x)−(y2+4y)=−60  4((x)2−2(x)(4)+42−42)−(y2+2(y)(2)+22−22)=−60  4((x)2−2(x)(4)+42−16)−(y2)+2(y)(2)+22−4=−60  4((x−4)2−16)−((y+2)2−4)=−60  4((x−4)2)−64−((y+2)2)+4=−60  4(x−4)2−(y+2)2=0  Step 2  The equations of the lines are 2x–y=10and2x+y=6  4(x−4)2−(y+2)2=0  [2(x−4)]2=(y+2)2  2x−8=(y+2)or2x−8=−(y+2)  2x−8=y+2or2x−8=−y−2  2x−y=10or2x+y=6  Step 3  Answer:  The equation represents pair of lines crossing each other at (4, -2) and the equations of the lines are 2x–y=10and2x+y=6

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

The exercise provides the equation for a degenerate conical section. Fill in the square and describe the graph of each equation.displaystyle{4}{x}{2}-{y}{2}-{32}{x}-{4}{y}+{60}={0}

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