**How to find equation of tangent to the curve :**

Here we are going to see how to find equation of tangent to the curve.

To find the equation of the tangent, we need to have the following things.

(i) a point on the curve on which the tangent line is passing through

(ii) Slope of the tangent line.

Note : We may find the slope of the tangent line by finding the first derivative of the curve.

**Step 1 :**

Find the value of dy/dx using first derivative.

Here dy/dx stands for slope of the tangent line at any point. To find the slope of the tangent line at a particular point, we have to apply the given point in the general slope.

**Step 2 :**

Let us consider the given point as (x_{1}, y_{1})

**Step 3 :**

By applying the value of slope instead of the variable "m" and applying the values of (x_{1} , y_{1}) in the formula given below, we find the equation of the tangent line.

(y - y_{1}) = m (x - x_{1})

Let us look into some example problems to understand the above concept.

**Example 1 :**

Find the equation of the tangent to the parabola y^{2} = 12x at the point (3, -6).

**Solution :**

y^{2} = 12x

Differentiate with respect to "x",

2y (dy/dx) = 12(1)

m = dy/dx = 12/2y ==> 6/y

Slope at the point (3, -6)

m = 6/(-6) ==> -1

**Equation of tangent :**

(y - y_{1}) = m (x - x_{1})

(y - (-6)) = (-1) (x - 3)

y + 6 = -x + 3

x + y + 6 - 3 = 0

x + y + 3 = 0

**Example 2 :**

Find the equation of the tangent to the parabola x^{2} + 2x - 4y + 4 = 0 at the point (0, 1).

**Solution :**

Equation of the curve is x^{2} + 2x - 4y + 4 = 0

Differentiate with respect to "x",

2x + 2(1) - 4 (dy/dx) + 0

4(dy/dx) = 2x + 2

dy/dx = 2(x + 1)/4

= (x + 1)/2

(dy/dx) _{at (0, 1)} = (0 + 1)/2 ==> 1/2

**Equation of tangent :**

(y - y_{1}) = m (x - x_{1})

(y - 1) = (1/2) (x - 0)

2y - 2 = x

x - 2y + 2 = 0

After having gone through the stuff given above, we hope that the students would have understood "How to find equation of tangent to the curve"

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