Student Activity

Tangents to Circles in Algebra 2 1.

2.

3.

4.

Given the circle x2 + y2 = 34 a)

Determine the coordinates of the points on the circle where x = 3.

b)

Let A be the point where x = 3 in the first quadrant. Determine the slope of the radius to point A.

c)

Write the equation of the tangent line to the circle at point A.

d)

Let B be the point where x = 3 in the fourth quadrant. Write the equation of the tangent line to the circle at point B.

e)

Determine the intersection of the two tangent lines.

Given the circle x2 + y2 = 34 a)

Determine the coordinates of the points on the circle where x = 5.

b)

Let P be the point where x = 5 in the first quadrant. Write the equation of the tangent line to the circle at point P.

c)

Let Q be the point where x = 5 in the fourth quadrant. Write the equation of the tangent line to the circle at point Q.

d)

Determine the intersection of the two tangent lines.

Given the circle x2 + y2 = 34 a)

Let M be a point in the first quadrant with coordinates (a, b). Let N be a point in the fourth quadrant with coordinates (a, -b). Conjecture what the coordinates of the intersection of the lines tangent to the circle at the points M and N would be.

b)

Show that your conjecture is true.

Let a circle centered at the origin, O, have a point P at (4, 2). a)

Write the equation for circle O.

b)

Determine the slope of OP .

c)

Write the equation of the line tangent to circle O at point P.

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Student Activity

5.

6.

Given the circle (x - 3 )2 + (y - 4 )2 = 5 a)

Verify that point P (4, 6) is on the circle.

b)

Write the equation of the line tangent to the given circle at P.

Let the line with the equation x – 2y = 15 and the circle with equation x2 + y2 = 50 intersect at the points A and B. a)

Find the coordinates of A and B using the given information.

b)

Graph the given equations and verify that your coordinates for A and B correspond to the graph.

c)

Determine the midpoint, M, of AB .

d)

Show that AB is perpendicular to the radius drawn through the midpoint, M, of AB .

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