Equation Of A Tangent To A Circle | Graphs | Maths | FuseSchool

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The equation of a circle is (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the centre of the circle and r is the radius. The coordinates of the centre point (a, b) are in the brackets with the x and y, but you just need to remember to change the sign of (a, b). On a circle, the tangent is always perpendicular to the radius. We use this key piece of information when finding the equation of the tangent. We then use our knowledge of the equation of a circle, and the equation of straight lines (y = mx + c) to find the equation of the tangent. If we know the centre is at (3, 2) and the tangent is at (6, -2) so we use this to find the gradient of the radius. If the gradient of the radius is -4/3 because the tangent is perpendicular to this, we can flip the gradient and change the sign, so the gradient of the tangent is 3/4. The equation of the tangent must be y equals ¾ x + c, where 'c' is the y-intercept. Then using the coordinates of the point on the circle which are (6, -2) for this example, substitute x is 6 and y is -2 in to find the missing y-intercept ‘c’ value. So the equation of the tangent is y = 34 x - 6.5.

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