First slide

Definition of a circle

Question

The tangent to $x^{2} + y^{2} = 9$ which is parallel to $y -$ axis and does not lie in the third quadrant touches the circle at the point

Moderate

A

$(3, 0)$
B

$(- 3, 0)$
C

$(0, 3)$
D

$(0, - 3)$

Solution

The equation of a tangent parallel to $y -$ axis is $x = c .$
This touches $x^{2} + y^{2} = 9 .$ Therefore, $c = \pm 3$ .
Thus, the equations of the tangents are $x = \pm 3 .$
Clearly, $x = 3$ is the tangent not lying in the third quadrant and it meets the circle at $(3, 0) .$

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