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

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

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