To identify: the conic section represented by each equation; write the equation in standard form and then graph the equation.

Expert Solution & Answer

Answer to Problem 13E

Parabola

(x−3)2=4⋅1(y−0)

Explanation of Solution

Given information:

x2−4y−6x+9=0

Calculation:

Rewrite the equation in the general form Ax2+Bxy+Cy2+Dx+Ey+F=0 to derive the coefficients as shown below.

1x2+0xy+0y2+(−6)x+(−4)y+9=0∴A=1 and C=0

Since C is zero. Thus, the conic section represented by the equation is a parabola.

The standard equation of a parabola is shown below.

(y−k)2=4p(x−h)or(x−h)2=4p(y−k)

Now rewrite the equation in the standard form as follows:

x2−4y−6x+9=0x2−6x=4y−9 [Rewrite the equation]x2−6x+9=4y−9+9(x−3)2=4y−0(x−3)2=4⋅1(y−0)

Thus, the standard equation of parabola is (x−3)2=4⋅1(y−0) .

The value of h,k and p is 3,0 and 1 respectively. The vertex (h,k) of parabola is (3,0) and focal length is 1. Thus, the graph of the given equation is shown below.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.6, Problem 13E

Chapter 10.6, Problem 12CFU

Chapter 10.6, Problem 14E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFU Ch. 10.1 - Prob. 2CFU Ch. 10.1 - Prob. 3CFU Ch. 10.1 - Prob. 4CFU Ch. 10.1 - Prob. 5CFU Ch. 10.1 - Prob. 6CFU Ch. 10.1 - Prob. 7CFU Ch. 10.1 - Prob. 8CFU Ch. 10.1 - Prob. 9CFU Ch. 10.1 - Prob. 10CFU

Ch. 10.1 - Prob. 11CFU Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.2 - Prob. 1CFU Ch. 10.2 - Prob. 2CFU Ch. 10.2 - Prob. 3CFU Ch. 10.2 - Prob. 4CFU Ch. 10.2 - Prob. 5CFU Ch. 10.2 - Prob. 6CFU Ch. 10.2 - Prob. 7CFU Ch. 10.2 - Prob. 8CFU Ch. 10.2 - Prob. 9CFU Ch. 10.2 - Prob. 10CFU Ch. 10.2 - Prob. 11CFU Ch. 10.2 - Prob. 12CFU Ch. 10.2 - Prob. 13CFU Ch. 10.2 - 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