Take this Exam: Higher Maths: the straight line and the circle | Zestly

Question 1

Does the point $(6, 1)$ lie inside, on, or outside the circle $(x - 2)^2 + (y + 1)^2 = 25$?

Accepted Answer

Inside the circle

Answer

On the circle

Answer

Outside the circle

Answer

At the centre of the circle

Question 2

A circle has centre $(1, 3)$, and a tangent touches it at the point $(4, 7)$. What is the gradient of that tangent?

Accepted Answer

$-\frac{3}{4}$

Answer

$\frac{4}{3}$

Answer

$\frac{3}{4}$

Answer

$-\frac{4}{3}$

Question 3

What is the midpoint of the line joining $A(-3, 8)$ and $B(5, -2)$?

Accepted Answer

$(1, 3)$

Answer

$(2, 6)$

Answer

$(4, -5)$

Answer

$(1, 5)$

Question 4

A triangle has vertices $A(2, 1)$, $B(6, 3)$ and $C(0, 7)$. What is the equation of the median from $A$?

Answer

$y = \frac{1}{4}x + \frac{1}{2}$

Answer

$y = 4x - 9$

Answer

$y = 4x - 7$

Answer

$y = -4x + 9$

Question 5

How many points does the line $y = x + 4$ have in common with the circle $x^2 + y^2 = 8$, and what does that make the line?

Answer

Two points, and the line passes through the centre

Answer

One point, so the line is a tangent to the circle

Answer

Two points, so the line is a chord of the circle

Answer

No points, so the line misses the circle entirely