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Find the equation of circle whose centre is (3,-1) and which cuts off an intercept of length 6 from the line 2x - 5y + 18 = 0.
You should remember the equation of circle in standard form such that:
The problem provides the coordinates (h,k) of center of circle, hence, you should substitute 3 for h and -1 for k in equation above such that:
Notice that the radius is not given but you may find it using the information provided by the problem.
The line that has the equation and the length of 6 represents a chord of circle.
You may drop a perpendicular from the center of circle to this chord. The perpendicular line drops in the middle of this chord.
You may find the length of perpendicular using the formula:
Notice that ax+by+c represents the equation of chord and , coordinates of the center.
Notice that the radius of circle represents the hypotenuse of right angle triangle that has the lengths of the legs and 3.
Using Pythagorean theorem yields:
You may now write the equation of the circle such that:
Hence, evaluating the equation of circle under given conditions yields
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