Which graph represents the circle given by the equation x + y - 4x + 9y -7 = 0?

Mathematics

1 answer:

PSYCHO15rus [73]2 years ago

5 0

The graph of the circle equation is graph (d)

<h3>How to determine the circle?</h3>

The equation is given as:

x^2 + y^2 - 4x + 9y -7 = 0

Rewrite as:

x^2 - 4x + y^2 + 9y = 7

Express (x^2 - 4x) and (y^2 + 9y) as perfect squares.

So, we have:

(x - 2)^2 + (y + 3)^2 = 7 + 4 + 20.25

Evaluate the sum

(x - 2)^2 + (y + 3)^2 = 31.25

A circle equation is represented as:

(x - h)^2 + (y - k)^2 = r^2

Where

Center = (h, k)

Radius = r

So, we have:

(h, k) = (2, -3)

r^2 = 31.25

r = 5.5

The circle that has a center of (2, -3) and a radius of 5.5 is graph d

Hence, the graph of the circle equation is graph (d)

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