First slide

Definition of a circle

Question

A circle is described on the line joining the points $(2, - 3)$ and $(- 4, 7)$ as a diameter

Easy

A

passes through the origin
B

touches the axis of x.
C

touches the axis of $y$
D

origin lies inside the circle

Solution

Equation of the circle is
$\begin{array}{l} (x - 2) (x + 4) + (y + 3) (y - 7) = 0 \\ \Rightarrow x^{2} + y^{2} + 2 x - 4 y - 29 = 0 \end{array}$
Centre is (1, – 2), radius $= \sqrt{34}$
Distance of the centre from the origin is $\sqrt{5} < \sqrt{34}$

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