Question

How to get the general equation of tangent to a circlr?

Answer 1

Work out the gradient of the radius at the point the tangent meets the circle, and you can use the equation mCP x mtgt = -1 to find the gradient of the tangent. Find the equation of the tangent to the circle at the point P(5, -2) which lies on the circle.

Answer 2

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The tangent to a circle

Finding the equation of a tangent to a circle

Finding the equation of a tangent to a circle is unlike finding a tangent to a polynomial. Because a tangent is a straight line, you need both a point and the gradient to find its equation. You are usually given the point - it's where the tangent meets the circle.

The method for finding the gradient uses the fact that the tangent is perpendicular to the radius from the point it meets the circle. Work out the gradient of the radius at the point the tangent meets the circle, and you can use the equation mCP x mtgt = -1 to find the gradient of the tangent.



Find the equation of the tangent to the circle  at the point P(5, -2) which lies on the circle.

centre = (1,1)



hence  since 

so equation of the tangent at P is



hope it help u