# EQUATION OF TANGENT AND NORMAL TO THE CURVE WORKSHEET

Find the equation of tangent and normal to the curve at the given point.

Problem 1 :

y = x – 2x2 + 3 at x = 2

Solution

Problem 2 :

y = √x + 1 at x = 4

Solution

Problem 3 :

y = x3 - 5x at x = 1

Solution

Problem 4 :

y = 4/√x at (1, 4)

Solution

Problem 5 :

Solution

Problem 6 :

y = 3x2 - 1/x at x = -1

Solution

1)  7x + y - 11 = 0, x - 7y - 23 = 0

2)  x - 4y + 8 = 0, 4x + y - 19 = 0

3)  2x + y + 2 = 0,  x - 2y - 9 = 0

4)  2x + y - 6 = 0, x - 2y + 7 = 0

5)  5x + y + 9 = 0, x - 5y - 21 = 0

6)  5x + y + 1 = 0, x - 5y + 21 = 0

Problem 1 :

Show that the line y = -3x - 10 is the tangent to the circle

x2 + y2 - 8x + 4y - 20 = 0

and also find the point of contact.

Solution

Problem 2 :

The circle

x2 + y2 + 4x - 7y - 8 = 0

cuts the y-axis at two points. Find the coordinates of these points.

Solution

Problem 3 :

The circle

x2 + y2 - 2x + 10y - 24 = 0

cuts the x-axis at the points A and B. Find the length of AB.

Solution

1)  (-2, -16)

2)  (0, 8) and (0, -1)

3)  A(6, 0) and B(-4, 0)

Problem 1 :

Find the points where the line with equation y = 3x intersects the circle with equation x2 + y2 = 20.

Solution

Problem 2 :

Find the points where the line with equation y = 2x + 6 and circle with equation x2 + y2 + 2x + 2 y − 8 = 0 intersect.

Solution

Problem 3 :

Find the points of intersection of the line y = 2x + 8 and the circle with equation x2 + y2 + 4x + 2y – 20 = 0.

Solution

Problem 4 :

Find the points of intersection of the circle

x2 + y2 – 2x – 4y + 1 = 0

and the line

x + y = 1.

Solution

1)  (√2, 3√2) and (-√2, -3√2).

2)  (-2, 2) and (-4, -2).

3) (-6, -4) and (-2, 4).

4)  (1, 0) and (-1, 2).

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