Question

focus and 2-5 r = 5.5-irs Since the radius is an imaginary value, the equation is not a real che point and focus Complete the squares for each quadratic, list the center and radius, then graph each od Determine which of the following equations represents a circle with a real non-zero radio x2 + y - 4x = 0 x² + y² - 2x - 8y=8 4x² + 4y² (h) 2 + y2 -7y=0 x2 + y2 - 2ax +2y=c (a) x2 + y2 + 10x = -30 (c) (b) 3x² + 3y² - 11x = -91 422 A.,2 Exercises 12.3 Complete the following: 1. labeling its translated center: (a) x² + 2x + y² – 4y = 4 (c) 2x² + 2y² + 3x - 5y=2 x² + y² + 3x = 4 x2 + y2 + 4x = 0 x2 + y2 + 2mx - 2ny = 0 latus red curvatus and poin Achar always 16x + 24 = -27 equation 2. is the locus the direct Select 10 125 the focus Figure 1

Answer 1

We will determine if the functions represent a circle with a real non-zero radius as follows:

b)

$3x^2+3y^2-11x=-91$

So, we try to factor it to determine the nature of the quadratic equation and since it cannot be factored or even plotted, we will have that it is not a circle with a real non-zero radius.

c)

$4x^2+4y^2+18x-8y=-85$

So, we try to factor it:

$\Rightarrow2(2x^2+9x+2y^2-4y)=-85$

We can factor in a limited fashion, but we can conclude that it is not a circle with a non-zero radius given the nature of the factorization.