Question

find the equation of tangents to the circle x2+y2=4 making an angle of 60 with positive x-axis in anticlockwise direction

Answer 1

hope it help you dear....

Answer 2

y = √3x - 2√3 and y = √3x + 2√3

Step-by-step explanation:

Let us assume that the point on the circle is (h,k).

So, h² + k² = 4 ............ (1)

Now, the equation of the circle is x² + y² = 4

Differentiating with respect to x both sides we get,

$2x + 2y \frac{dy}{dx} = 0$

⇒ $\frac{dy}{dx} = - \frac{x}{y}$

Now, at point (h,k) the slope is $- \frac{h}{k} = \tan 60^{\circ} = \sqrt{3}$

⇒ h = - √3k ....... (2)

From, equation (1) we get

(-√3k)² + k² = 4

⇒ 3k² + k² = 4

⇒ k² = 1

⇒ k = ± 1

Now, for k = 1. h = - √3 and for k = - 1, h = √3 {From equation (2)}

Therefore, the equation of the tangent to the circle at points (1,-√3) ans (-1,√3) will be

(y + √3) = √3(x - 1) = √3x - √3

⇒ y = √3x - 2√3 (Answer)

And, (y - √3) = √3(x + 1) = √3x + √3

⇒ y = √3x + 2√3 (Answer)