Question

If r represents the distance of a point from origin & θ is the angle made by line joining origin to that point from line x-axis , then r = ∣cosθ∣ represents:

Answer 1

Correct options are (A), (B) and (C)

\(r =|\cos \theta|\)

\(r = \sqrt{(x - 0)^2 +(y - 0)^2 }\)

\(= \sqrt{x^2 + y^2}\)

\(\cos \theta = \frac{OM}{OP} = \frac xr = \frac{x}{\sqrt{x^2 + y^2}}\)

\(r = \sqrt{x^2 + y^2} =\left |\frac x{\sqrt {x^2 + y^2}}\right|\)

\(\sqrt{x^2 + y^2} = \frac x{\sqrt{x^2 + y^2}}\)

⇒ \(x^2 + y^2 = x\)

⇒ \(x^2 + y^2 - x =0\)

centre = \((\frac 12,0)\)

rad = 1/2

\(\sqrt{x^2 + y^2} = \frac {-x}{\sqrt{x^2 + y^2}}\)

⇒ \(x^2 + y^2 = -x\)

⇒ \(x^2 + y^2+ x =0\)

centre = \((-\frac 12,0)\)

rad = 1/2