# Lesson Worksheet: The Equation of a Tangent to a Circle Mathematics • 11th Grade

In this worksheet, we will practice finding the equation of a tangent to a circle using the coordinates of the circle’s center and a point of tangency.

Q1:

Suppose that is a diameter of a circle center . If , what is the general equation of the tangent to the circle at ?

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Q2:

A circle with center has a diameter , where is on the circumference. Given that the coordinates of the points and are and , respectively, determine the equation of the tangent to the circle at the point .

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Q3:

The equation of the given graph is . Find the equation of the tangent at the point . • A
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Q4:

For the equation find the equation of the tangent at the point .

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Which of the following is the graph of the circle along with the tangent line found in the first part?

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A circle has the equation . Find the gradient of the tangent at the point .

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Q6:

Suppose that is a diameter at a circle with center , where and . What is the general equation of the tangent to the circle at ?

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Q7:

A circle has the equation . Find the gradient of the tangent at the point .

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Q8:

A circle has the equation . If the equation of a tangent at point is found to be , find .

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Q9:

Determine the equation of the tangent to the circle at the point .

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Q10:

Which of the following graphs represents the circle and the tangent with gradient ?

• A • B • C • D • E This lesson includes 6 additional questions and 117 additional question variations for subscribers.