Given the function x2 + y2 = 25. If the equation is an equation of a circle, center at the origin, find the slope of the tangent line along the circumference at the tangent point (-2, 5).?
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Slope of the tangent: 2/5
Step-by-step explanation:
Equation of the circle: x²+y²=25
Center of the circle is (0,0)
slope of the line joining the centre and the point (-2,5) where the tangent touches the circle = -5/2
hence slope of the tangent = 2/5 ( since it is perpendicular to the line joining the centre and the point (-2,5) where the tangent touches the circle)
Another Method ( BY THE APPLICATION OF DERIVATIVES)
Equation of the circle : x²+y²=25
differentiating the equation in both sides with respect to x, we get,
2x+2yy' = 0
y' = -2x/2y
= -x/y
y' is the slope of tangent at any of the circle x²+y²=25
slope of the tangent at (-2,5) , y' at (-2,5) = 2/5
Slope of the required tangent is 2/5
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