Chapter 11: Q. 310 (page 1159)

In the following exercises, identify the type of graph.
$(a) x^{2} + y^{2} + 4 x - 10 y + 25 = 0 (b) y^{2} - x^{2} - 4 y + 2 x - 6 = 0 (c) x = - y^{2} - 2 y + 3 (d) 16 x^{2} + 9 y^{2} = 144$

Short Answer

Expert verified

The equation represents

(a) Circle

(b) Hyperbola

(d) ellipse

Step by step solution

Step 1. Given Information

The given equations are

$(a) x^{2} + y^{2} + 4 x - 10 y + 25 = 0 (b) y^{2} - x^{2} - 4 y + 2 x - 6 = 0 (c) x = - y^{2} - 2 y + 3 (d) 16 x^{2} + 9 y^{2} = 144$

Part (a) Step 1. Explanation

From the given equation it is very clear that $x^{2} a n d y^{2}$ terms have same sign and same coefficient. So, the equation represents the Circle.

Part(b) Step 1. Explanation

From the given equation it is very clear that $x^{2} a n d y^{2}$ terms have different sign and different coefficient. So, the equation represents the hyperbola.

Part(c) Step 1. Explanation

From the given equation it is very clear that one variable $y$ is squared. So, the equation represents the Parabola.

Part(d) Step 1. Explanation

From the given equation it is very clear that $x^{2} a n d y^{2}$ terms have same sign and different coefficient. So, the equation represents an ellipse.

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In the following exercises, identify the type of graph.
$(a) x^{2} + y^{2} + 4 x - 10 y + 25 = 0 (b) y^{2} - x^{2} - 4 y + 2 x - 6 = 0 (c) x = - y^{2} - 2 y + 3 (d) 16 x^{2} + 9 y^{2} = 144$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Explanation

Part(b) Step 1. Explanation

Part(c) Step 1. Explanation

Part(d) Step 1. Explanation

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In the following exercises, identify the type of graph.(a)x2+y2+4x-10y+25=0(b)y2-x2-4y+2x-6=0(c)x=-y2-2y+3(d)16x2+9y2=144

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Explanation

Part(b) Step 1. Explanation

Part(c) Step 1. Explanation

Part(d) Step 1. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

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Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, identify the type of graph.
$(a) x^{2} + y^{2} + 4 x - 10 y + 25 = 0 (b) y^{2} - x^{2} - 4 y + 2 x - 6 = 0 (c) x = - y^{2} - 2 y + 3 (d) 16 x^{2} + 9 y^{2} = 144$