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junior college 2 | H3 Maths

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The centre of the circle is (-1,-2). Means it's in the negative part of both axes.

And the radius is 2 units.

When you draw the radius upwards from the centre (such that the radius is parallel to the y-axis), the point on the circle that you reach will be on the x-axis.

So y coordinate is 0.

( - 2 + 2 units upwards = 0 )

But your x coordinate remains unchanged at -1 since the radius is drawn parallel to the y-axis. So the tangent point is (-1,0).

Extend a line from the tangent point to the origin. You realise that this tangent is actually just the x-axis. So equation is

y = 0

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m1 = (y1 - y2) ÷ (x1 - x2)

= (0- (-2) ) ÷ (-1 - (-1) )

= 2 ÷ 0

→ undefined

- 1 = m1 x m2

m2 = -1 ÷ (2 ÷ 0)

m2 = - 1 x 0/2

= 0

(Usually, it's understood that if m1 is undefined then m2 is 0)

Check your circle drawing. If you draw the radius to the right of the centre , parallel to x-axis, the point will be (1, -2). So the circle should cut the y- axis.