Recall the equation for a circle with center ( h , k ) ( h , k ) and radius r r . At what point in the first quadrant does the lin

Question

Recall the equation for a circle with center ( h , k ) ( h , k ) and radius r r . At what point in the first quadrant does the line with equation y = 2 x + 1 y = 2 x + 1 intersect the circle with radius 5 and center (0, 1)?

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Doris 11 mins 2023-01-07T19:05:28+00:00 1 Answer 0 views 0

Answer ( 1 )

  1. Nho
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    2023-01-07T19:06:32+00:00
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    The point in the first quadrant at which the line intersects the circle is; ; (√5, 2√5+1).

    Which point in the first quadrant does the line intersects the circle?

    Since the equation of a circle whose radius is 5 and center is; (0, 1) is as follows;
    (x-0)² + (y-1)² = 5².
    Hence, since the line, y = 2x +1, intersects the circle in the first quadrant;
    By substitution, we have;
    x² + (2x+1-1)² = 25
    5x² = 25
    x² = 5.
    Hence, x = ±√5, more specifically, x = √5 in the first quadrant and hence, y = 2√5 +1.
    The required point is therefore; (√5, 2√5+1).
    Read more on equation of a circle;
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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )