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How do you find all the points that are 26.5 units away from the point 26 and the line y2?
Wiki User
∙ 6y ago
The set of points 26.5 units away from the point (2, 6) are those points that lie on the circle with centre (2, 6) and radius 26.5; this has equation:
(x - 2)² + (y - 6)² = 26.5²
The set of points 26.5 units away from the line y = 2 are those points which lie on the lines which are parallel to 26.5 and 2 units away, ie the lines y = 2 ± 26.5→y = -24.5 or y = 28.5
The points where these lines meet the circle are the required points.
By substituting the y values of the two lines into the equation for the circle and solving it will give you the required points.
That's HOW to find all the points.
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Solving the problem and finding the points:
- line y = -24.5
→ x² - 4x + 4 + 30.5² - 26.5² = 0
→ x² - 4x + 232 = 0
→ x = 2(1 ± √-57)
As the square root is of a negative number the line does not meet the circle - it has no points in common
- line y = 28.5
→ x² - 4x + 4 + 22.5² - 26.5² = 0
→ x² - 4x - 192 = 0
→ (x + 12)(x - 16) = 0
→ x = -12 or 16
→ points are (-12, 28.5) and (16, 28.5)
→ all the points that are 26.5 units away from the point (2, 6) and the line y = 2 are (-12, 28.5) and (16, 28.5).
Wiki User
∙ 6y ago
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