Find The Length Of A Tangent Segment From A(5,2) From The Circle X^2 + Y^2 = 13

Find the length of a tangent segment from A(5,2) from the circle x^2 + y^2 = 13

 

Answer: 4

Step-by-step explanation: Let the required length be L. We know that the graph of x²+y²=13 is a circle centered at (0,0) with radius √13. The distance between (0,0) and (5,2) is √29. Also, tangents are always perpendicular to the radius at the point of tangency. Drawing this, we will actually have a right triangle with hypotenuse √29 and legs L and √13. By the Pythagorean Theorem,

L²=(√29)²-(√13)²=29-13=16.

Therefore, L= 4


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