If the line $x cos θ + y sin θ = 2$ is the equation of a transverse common tangent to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} - 6 \sqrt{3} x - 6 y + 20 = 0$ , then the value of $θ$ is

\frac{5 π}{6}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 π}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{π}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{π}{6}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{π}{6}$
$C_{1} C_{2} = r_{1} + r_{2}$
$C_{1} = (0, 0); C_{2} = (3 \sqrt{3}, 3)$
and $r_{1} = 2, r_{2} = 4$
$\Rightarrow$ Circle touch each other externally.
Equation of common tangent is $\sqrt{3} x + y - 4 = 0$ ...... (i)
Comparing it with $x cos θ + y sin θ = 2$ , we get $θ = \frac{π}{6}$

Suggest Corrections

Similar questions

Q. If the line

x cos θ + y sin θ = 2

is the equation of a transverse common tangent to the circles

x^{2} + y^{2} = 4

and ,

x^{2} + y^{2} - 6 \sqrt{3} x - 6 y + 20 = 0

then the value of

θ

in degree is :

Q. If the tangent at

(θ)

to the circle

x^{2} + y^{2} = 4

touches the circle

x^{2} + y^{2} - 6 \sqrt{3} x - 6 y + 20 = 0

then one of the values of

θ

is?

Let $θ \in (0, \frac{π}{2}) a n d x = X c o s θ + y s i n θ, y = X s i n θ - Y c o s θ$ such that $x^{2} + 2 x y + y^{2} = a X^{2} + b Y^{2}$ Where a and b are constants then

The value of q, if the equation x cos θ + y sin θ = p is the normal form of the line √3x + y + 2 = 0 is:

Q. The number of common tangents to circles

x^{2} + y^{2} - 4 x + 2 y - 4 = 0

and

x^{2} + y^{2} + 2 x - 6 y + 6 = 0

Join BYJU'S Learning Program

If the line xcosθ+ysinθ=2 is the equation of a transverse common tangent to the circles x2+y2=4 and x2+y2−6√3x−6y+20=0, then the value of θ is

The correct option is D π6C1C2=r1+r2C1=(0,0);C2=(3√3,3)and r1=2,r2=4⇒ Circle touch each other externally.Equation of common tangent is √3x+y−4=0 ...... (i)Comparing it with xcosθ+ysinθ=2, we get θ=π6

If the line $x cos θ + y sin θ = 2$ is the equation of a transverse common tangent to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} - 6 \sqrt{3} x - 6 y + 20 = 0$ , then the value of $θ$ is