Gr12 Mathematics: Ch 6.2 Equation of a Tangent to a Circle

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What is the definition of a tangent line to a circle?

A straight line that touches the circle at exactly one point without crossing it (correct)

A straight line that is parallel to the circle

A straight line that touches the circle at exactly two points without crossing it

A straight line that crosses the circle at exactly two points

What is the relationship between the gradient of the radius and the gradient of the tangent at the point of tangency?

m_radius + m_tangent = 0

m_radius × m_tangent = -1 (correct)

m_radius ÷ m_tangent = 1

m_radius × m_tangent = 1

What is the first step in determining the equation of a tangent to a circle?

Write the equation of the circle in its standard form (correct)

Determine the gradient of the tangent

Find the center of the circle

Find the point of tangency

What is the formula for the gradient of the radius?

m_radius = (y_1 - b) / (x_1 - a) Signup and view all the answers

What is the equation of the tangent in terms of the gradient-point form?

y - y_1 = m_tangent (x - x_1) Signup and view all the answers

What is the purpose of finding the center of the circle?

To find the gradient of the radius Signup and view all the answers

Why is the gradient of the radius perpendicular to the gradient of the tangent?

Because they are perpendicular lines Signup and view all the answers

What is the final step in determining the equation of a tangent to a circle?

Write down the gradient-point form of the straight line equation Signup and view all the answers

What is the coordinate of the center of the circle given by the equation (x - 3)^2 + (y - 4)^2 = 16?

(3, 4) Signup and view all the answers

What is the gradient of the radius when the point of tangency is (5, 7) and the center of the circle is (3, 4)?

3/2 Signup and view all the answers

What is the gradient of the tangent when the gradient of the radius is 3/4?

-4/3 Signup and view all the answers

A circle has its center at (2, 5) and a radius of 3 units. What is the equation of the tangent at the point (5, 7)?

y - 7 = (1/3)(x - 5) Signup and view all the answers

A tangent is drawn to a circle at the point (7, 3) and the center of the circle is (4, 2). What is the equation of the tangent?

y - 3 = (-1/3)(x - 7) Signup and view all the answers

What is the relationship between the gradient of the radius and the gradient of the tangent at the point of tangency?

Their product is -1 Signup and view all the answers

What is the use of finding the center of the circle in determining the equation of the tangent?

To find the gradient of the radius Signup and view all the answers

What is the purpose of finding the gradient of the radius in determining the equation of the tangent?

To find the gradient of the tangent Signup and view all the answers

What is the coordinate of the point of tangency if the equation of the circle is (x - 2)^2 + (y - 3)^2 = 25 and the gradient of the radius is 2/3?

(5, 7) Signup and view all the answers

If the gradient of the tangent is -3/4, what is the gradient of the radius?

4/3 Signup and view all the answers

What is the equation of the tangent at the point (3, 4) if the center of the circle is (2, 3) and the radius is 5 units?

y - 4 = (3/4)(x - 3) Signup and view all the answers

If the equation of the circle is x^2 + y^2 - 4x - 6y + 4 = 0, what is the center of the circle?

(2, 3) Signup and view all the answers

What is the gradient of the radius if the point of tangency is (6, 5) and the center of the circle is (4, 3)?

2/3 Signup and view all the answers

If the equation of the tangent is y - 5 = (2/3)(x - 4), what is the point of tangency?

(4, 5) Signup and view all the answers

What is the radius of the circle if the equation of the circle is (x - 3)^2 + (y - 4)^2 = r^2 and the point of tangency is (6, 5)?

5 Signup and view all the answers

If the gradient of the tangent is -2/5, what is the equation of the tangent at the point (3, 4) if the center of the circle is (2, 3)?

y - 4 = (-2/5)(x - 3) Signup and view all the answers

Gr12 Mathematics: Ch 6.2 Equation of a Tangent to a Circle

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Questions and Answers

What is the definition of a tangent line to a circle?

What is the relationship between the gradient of the radius and the gradient of the tangent at the point of tangency?

What is the first step in determining the equation of a tangent to a circle?

What is the formula for the gradient of the radius?

What is the equation of the tangent in terms of the gradient-point form?

What is the purpose of finding the center of the circle?

Why is the gradient of the radius perpendicular to the gradient of the tangent?

What is the final step in determining the equation of a tangent to a circle?

What is the coordinate of the center of the circle given by the equation (x - 3)^2 + (y - 4)^2 = 16?

What is the gradient of the radius when the point of tangency is (5, 7) and the center of the circle is (3, 4)?

What is the gradient of the tangent when the gradient of the radius is 3/4?

A circle has its center at (2, 5) and a radius of 3 units. What is the equation of the tangent at the point (5, 7)?

A tangent is drawn to a circle at the point (7, 3) and the center of the circle is (4, 2). What is the equation of the tangent?

What is the relationship between the gradient of the radius and the gradient of the tangent at the point of tangency?

What is the use of finding the center of the circle in determining the equation of the tangent?

What is the purpose of finding the gradient of the radius in determining the equation of the tangent?

What is the coordinate of the point of tangency if the equation of the circle is (x - 2)^2 + (y - 3)^2 = 25 and the gradient of the radius is 2/3?

If the gradient of the tangent is -3/4, what is the gradient of the radius?

What is the equation of the tangent at the point (3, 4) if the center of the circle is (2, 3) and the radius is 5 units?

If the equation of the circle is x^2 + y^2 - 4x - 6y + 4 = 0, what is the center of the circle?

What is the gradient of the radius if the point of tangency is (6, 5) and the center of the circle is (4, 3)?

If the equation of the tangent is y - 5 = (2/3)(x - 4), what is the point of tangency?

What is the radius of the circle if the equation of the circle is (x - 3)^2 + (y - 4)^2 = r^2 and the point of tangency is (6, 5)?

If the gradient of the tangent is -2/5, what is the equation of the tangent at the point (3, 4) if the center of the circle is (2, 3)?

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