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

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Equation of a Tangent to a Circle
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At how many points does a tangent touch the circumference of a circle?

Exactly one point

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

They are perpendicular

What angle is formed between the radius and tangent at the point of tangency?

90°90°

If mradius×mtangent=−1m_{\text{radius}} \times m_{\text{tangent}} = -1, what does this tell us?

The lines are perpendicular

If the radius has gradient 33, what is the gradient of the tangent?

−13-\frac{1}{3}

In the equation (x+5)2+(y−2)2=16(x + 5)^2 + (y - 2)^2 = 16, what are the centre coordinates?

(−5;2)(-5; 2)

Which form is used to write the equation of the tangent?

y−y1=m(x−x1)y - y_1 = m(x - x_1)

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

Write equation in standard form

Tangents parallel to y=4x+7y = 4x + 7 have what gradient?

44

From centre (0;1)(0; 1) to point (4;−7)(4; -7), what is the gradient of the radius?

−2-2

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