Equation of a Circle and Finding the Tangent

The video tutorial covers the equation of a circle, starting with the basic formula x^2 + y^2 = r^2. It explains how to find the radius from the equation and provides examples. The tutorial then demonstrates using Pythagoras' theorem to calculate the radius and equation of a circle. Finally, it explains how to find the equation of a tangent to a circle, including calculating gradients and using the negative reciprocal for perpendicular lines.

What is the general formula for the equation of a circle?

• x^2 + y = r^2

• x + y = r^2

• x^2 + y^2 = r^2

• x^2 + y^2 = r

If the equation of a circle is x^2 + y^2 = 49, what is the radius of the circle?

• 7

• 49

• 14

• 24.5

How can you calculate the radius of a circle using Pythagoras' theorem?

• By adding the x and y coordinates

• By subtracting the x coordinate from the y coordinate

• By using the formula x^2 + y^2 = r^2

• By finding the square root of the sum of the squares of the triangle's sides

What is the gradient of a tangent if the gradient of the radius is 4/3?

• 4/3

• 3/4

• -4/3

• -3/4

Which equation represents a straight line graph?

• x = my + c

• y = x^2 + c

• x^2 + y^2 = r^2

• y = mx + c