Question

(6.) The point A(-5,12) lies on the circle whose equation is x + y2 = 169. What is the secant of

Answer 1

The secant of the angle through a point (-5, 3) is -13/5  

Equation of a circle

The equation of a circle with center (0,0) is given by

x² + y² = r² where r = radius of circle

Now, comparing this to the equation of the given circle x² + y² = 169,

⇒ r² = 169

r = √169

r = 13

Secant of angle

The secant of the angle through a point (x, y) is secФ = r/x where

• r = radius of circle and
• x = x-coordinate of point

Now for the point A(-5,12), x = -5.

Since r = 13

secФ = r/x

= 13/-5

= -13/5  

So, The secant of the angle through a point (-5, 3) is -13/5  

Learn more about secant of an angle here:

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