
To match:
The equation with one of the graphs (a)-(d).

Answer to Problem 1CT
Solution:
(c).
Explanation of Solution
Given:
The equation
The graphs a-d.
Concept:
Observe the given equation and check if it is of parabola,
If the given equation is quadratic for coefficient of
If the given equation is quadratic for coefficients of both
Else if the given equation is quadratic for coefficients of both
For parabola, follow the following steps:-
(i) Rewrite the given equation in standard form of parabola
where the vertex is
(ii) If
If
If
If
(iii) If vertex is origin
(iv) If center is not origin, then find the quadrant in which the vertex of the given equation lies.
(v) Match the quadrant found with the graph from options a-d having vertex as
For hyperbola, follow the following steps: -
(i) Rewrite the given equation in standard form of hyperbola with center at
(ii) If the given equation is of form
Else if the given equation is of form
(iii) Match the hyperbola with the graph with transverse axis as horizontal or vertical.
For ellipse or circle, follow the following steps: -
(i) Rewrite the given equation in standard form of ellipse with center at
and major axis length is
(ii) If
If
Else if
(iii) If center is origin
(iv) If center is not origin, then find the quadrant in which the center point of the given equation lies.
(v) Match the quadrant found with the graph from options a-d having center as
Calculation:
Since given equation
(i) Rewrite the given equation in standard form of hyperbola with center at
Hence the given equation
Dividing by
Simplifying,
The center is
(ii) Since
(iii) Observing the graphs for hyperbola with center as
Hence the graph of the equation
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Chapter 7 Solutions
College Algebra (5th Edition)
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