Given that we find the values of ‘m’ such that y = mx does not intersect the circle (x + 10)² + (y + 10)² = 180

The line does not intersect the circle if the perpendicular distance between the centre and the line is greater than the radius of the circle.

Here the centre and radius of the circle is (- 10, - 10) and √180.

We know that the perpendicular distance from the point (x₁,y₁)to the line ax + by + c = 0 is .

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⇒ 100 - 200m + 100m²>180 + 180m²

⇒ 80m² + 200m + 80<0

⇒ 2m² + 5m + 2<0

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We know that the solution set for the inequality (x - a)(x - b)<0 is (a, b) for b>a.

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∴The solution set for ‘m’ is .