Question

The equation of tangents to the circle x²+y²=4 which are parallel to the x-axis are

Answer 1

Answer:

y = √3x - 2√3 and y = √3x + 2√3

Step-by-step explanation:

So, h² + k² = 4 ............ (1)

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

Differentiating with respect to x both sides we get,

⇒

Now, at point (h,k) the slope is

⇒ 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)

Hope it helps