Question

Determine if the following statements are true or false. motivate your answer!
a). The equation x^2+y^2-2<0
b). The slope of a straight line can't be equal to zero.
c). If /a/=/b/, then a=b

Answer 1

a) False. The equation x^2+y^2-2=0 is an equation for circle of radius sqrt(2).
x^2+y^2-2>0 indicates the equation for circles with radii greater than root of 2. So the equation is not true

b)False. The slope of a straight line is the tan of the angle it makes with x axis. For a straight line which makes an angle 0 with x axis(a straight line parallel to the x axis or x axis itself), the tan value is 0.

c)False. A and b could be different signs, and still their mod values would be the same. Eg. a=-5, b=5, /a/=5; /b/=5 but a not equal to b