Question

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0, 7). Which statement must be true?

Answer 1

The true statement is the circle has the radius equal to 7.

What is Equation of circle?

The general equation for a circle is (x-h)² + (y-k)² = r², where ( h, k ) is the center and r is the radius.

As, standard form of equation of circle is

(x-h)² + (y-k)² = r²

At origin, equation of circle will be

(0-h)² + (0-k)² = r²

r² = x² + y²

Now, The line intersects the circle at (0,7)

r² = 0² + 7²

r² =49

r=7.

Hence, the circle has the radius equal to 7.

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