Equation of a Tangent to a Circle (Grade 12 NSC Matric Mathematics): Flashcards

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Equation of a Tangent to a Circle
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Tangent to a circle

Line touching circle at exactly one point

Point of tangency

Point where tangent meets the circle

Radius to tangency point vs tangent

Always perpendicular

Angle between radius and tangent

90°90°

Product of perpendicular gradients

m1imesm2=−1m_1 imes m_2 = -1

mextradiusimesmexttangentm_{ ext{radius}} imes m_{ ext{tangent}}

−1-1

Standard form of circle equation

(x−a)2+(y−b)2=r2(x - a)^2 + (y - b)^2 = r^2

Centre from (x−a)2+(y−b)2=r2(x - a)^2 + (y - b)^2 = r^2

(a;b)(a; b)

mexttangentm_{ ext{tangent}} from mextradiusm_{ ext{radius}}

- rac{1}{m_{ ext{radius}}}

Point-slope form

y−y1=m(x−x1)y - y_1 = m(x - x_1)

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