ESAT (Engineering and Science Admissions Test) · Mathematics 2

Coordinate geometry

6 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 6 questions

A circle has equation $x^{2} + y^{2} - 6 x + 4 y - 12 = 0$ . What are its centre and radius?
The line $y = 2 x + k$ is a tangent to the circle $x^{2} + y^{2} = 5$ . What are the possible values of $k$ ?
A triangle has vertices $(1, 1)$ , $(7, 3)$ and $(3, 7)$ . What is its area?
What is the equation of the tangent to the circle $x^{2} + y^{2} = 25$ at the point $(3, 4)$ ?
The points $A (1, 2)$ and $B (5, 8)$ are given. What is the equation of the perpendicular bisector of $A B$ ?
Two circles have centres $(0, 0)$ with radius $3$ , and $(8, 6)$ with radius $7$ . How are they related?

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