Identify this conic section. x 2 + y 2 = 25 line circle ellipse parabola hyperbola

circle

Step-by-step explanation:

The equation

x² + y² = r²

Represents a circle centred at the origin with radius r

x² + y² = 25 ← is in this form and

is a circle centre (0, 0) with r = 5

ANSWER

circle

EXPLANATION

The given equation is

To determine the type of conic, we analyze the coefficient and sign of the quadratic terms.

If the coefficient of the quadratic terms are equal and have the same sign,then the conic is a circle.

If the coefficient of the quadratic terms are equal and have opposite signs,then the conic is a hyperbola.

If the coefficient of the quadratic terms are not equal and have the same sign,then the conic is an ellipse.

Since the coefficients are all 1 and the signs are positive, the given conic is a circle.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

there are infinitely many solutions.