   Chapter 10.1, Problem 94E

Chapter
Section
Textbook Problem

# True or False? In Exercises 87-92, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If D ≠ 0 or E ≠ 0 , then the graph of y 2 − x 2 + D x + E y = 0 is a hyperbola.

To determine
Whether the statement “If D0 or E0 then the graph of y2x2+Dx+Ey=0 is a hyperbola” is true or false.

Explanation

Consider the equation y2x2+Dx+Ey=0.

Rewrite the equation as,

y2x2+Dx+Ey=0(x2+2(12)(Dx)D24+D24)+(y2+2(12)(Ex)+E24E24)=0(x22(12)(Dx)+D24)+D24+(y2+2(12)(Ex)+E24)E24=0(y+E2)2(xD2)2=E24D24

Simplify the above equation,

(y+E2)2(E24D24)(xD2)2(E24D24)=1

The above equation is not an equation of hyperbola when D0 or E0

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