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Chapter 11: Q. 343 (page 1160)

Identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola b) write the equation in standard form and c) graph the equation.

9x2-25y2-36x-50y-214=0

Short Answer

Expert verified

The Graph of the equation is hyperbola.

Step by step solution

01

Step 1. Given Information

Given that the equation is9x2-25y2-36x-50y-214=0.

02

Step 2. Form of the equation

There is a different sign of x2ory2and different coefficient. Hence, the equation is hyperbola.

03

Step 3. Standard form of hyperbola

On rewriting the equation,

9x2-25y2-36x-50y=2149(x-2)2214-25(y+1)2214=1h=2,k=-1a=214,b=214Here,x2ispositive.Thehyperbolawillopenrightandleft.

Thus, the solution is9(x-2)2214-25(y+1)2214=1.

04

Step 4. Graph of the hyperbola

On drawing the graph of the equation,

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