Question

What are the equations of the lines that pass through the point P(-3,-2) and the circle with radius r = 5 and center M(4,-1)?

Answer #1

What are the equations of the lines that pass through the point
P(-3,-2) and the circle with radius r = 5 and center M(4,-1)?

What are the equations of the lines that pass through the point
P(-3,-2) and that touch (tangent to) the circle with radius r = 5
and center M(4,-1)?

Determine the equations of two lines that pass through the point
(-1,-3) and are tangent to the graph of y=x2+1.

1. Given a circle centered at C with a
radius of r and a point P outside of the circle. If segment PT is
tangent to the circle at T show that the power of point P with
respect to the circle is equal to PT squared.

A
circle has radius 2 and center (0, 0). A point P begins at (2, 0)
and moves along the circumference of this circle in the
counterclockwise direction. It moves with constant angilar velocity
2.7 radians per second.
Let s be the arc in standard position whose terminal point is
P.
What is s in terms of t, the number of seconds since P began
moving?
What are the coordinates of P in terms of s?
What are the coordinates...

1) Show that the formulas below represent the equation of a
circle.
x = h + r cos θ
y = k + r sin θ
2) Use the equations in the preceding problem to find a set of
parametric equations for a circle whose radius is r = 4 and whose
center is (-1,-2).
3) Plot each of the following points on the polar
plane. A(2, π/4), B(1, 3π/2), C(4, π)

1.Let y=6x^2. Find a parametrization of the
osculating circle at the point x=4.
2. Find the vector OQ−→− to the center of the
osculating circle, and its radius R at the point
indicated. r⃗
(t)=<2t−sin(t),
1−cos(t)>,t=π
3. Find the unit normal vector N⃗ (t)
of r⃗ (t)=<10t^2, 2t^3>
at t=1.
4. Find the normal vector to r⃗
(t)=<3⋅t,3⋅cos(t)> at
t=π4.
5. Evaluate the curvature of r⃗
(t)=<3−12t, e^(2t−24),
24t−t2> at the point t=12.
6. Calculate the curvature function for r⃗...

The diagram shows a circle C1 touching a circle C2 at a point X.
Circle C1 has center A and radius 6 cm, and circle C2 has center B
and radius 10 cm. Points D and E lie on C1 and C2 respectively and
DE is parallel to AB. Angle DAX = 1/3? radians and angle EBX = ?
radians.
1) By considering the perpendicular distances of of D and E from
AB, show that the exact value of ?...

1. A point is chosen at random in the interior
of a circle of radius R. The probability that the point falls
inside a given region situated in the interior of the circle is
proportional to the area of this region. Find the probability
that:
a) The point occurs at a distance less than r
(r>R) from the center
b) The smaller angle between a given direction
and the line joining the point to the center does not exceed α.

Section 1.3 The Intersection Point of a Pair of Lines
Solve the systems of linear equations
! ) 4( ? ? + + 2? ) ( ? = = 3
!? ? − + - ( 2? ? = = 4 6

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