First slide

Definition of a circle

Question

Tangents are drawn from a point on the circle
$x^{2} + y^{2} - 4 x + 6 y - 37 = 0$ to the circle $x^{2} + y^{2} - 4 x + 6 y - 12 = 0$
The angle between the tangents, is

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{3}$
C

$\frac{π}{6}$
D

$\frac{π}{2}$

Solution

the equations of the circles are:
$(x - 2)^{2} + (y + 3)^{2} = (5 \sqrt{2})^{2} . . . . . . . (i)$
and $(x - 2)^{2} + (y + 3)^{2} = 5^{2} (i i)$
Clearly, (i) is the direction circle of (ii). So, required angle is $\frac{π}{2}$

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