FIND POINT OF CONTACT OF TANGENT AND CIRCLE WORKSHEET

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.

Problem 2 :

The circle

x² + y² + 4x - 7y - 8 = 0

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

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.

Answer Key

1) point of contact is (-2, -16).

2) points of contact are (0, 8) and (0, -1).

3) points of intersection are 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.

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.

Problem 3 :

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

Problem 4 :

Find the points of intersection of the circle

x² + y² – 2x – 4y + 1 = 0

and the line

x + y = 1.

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).