Math CentralQuandaries & Queries


Question from AHMED, a student:

find the equation to the circle with centre at the point (1,-1) and touching the straight line 5x+12y=7.

Hi Ahmed,

Since the line 5x + 12y = 7 only touches the circle it is a tangent to the circle. Suppose the point of tangency has coordinated (a, b). Since (a, b) is on the line

5a + 12b = 7.

The key to this problem is the fact that the line segment from (1, 1) to (a, b) is perpendicular to the line 5x + 12y = 7. What is the slope of the line segment from (1, 1) to (a, b)?

Can you complete the problem?

Write back if you need more help,

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